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这一问题,人工去计算的话,将会非常非常地复杂!不过我们可以利用数学软件。 我用的是Matlab,它能解决许多问题包括解一元四次方程。 由于此软件在定义n、V、C时把n当成了常量处理,因此用x代替。第一张图是测试。 以下的答案是把n当变量,V、C为常量,四个根的结果如下: ans: n1=1/2+1/6*3^(1/2)/v*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)+1/6/v*(-3/v*(-2*v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-4*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2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n2=1/2+1/6*3^(1/2)/v*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-1/6/v*(-3/v*(-2*v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-4*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2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n3=1/2-1/6*3^(1/2)/v*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)+1/6/v*(-3/v*(-2*v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-4*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2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n4=1/2-1/6*3^(1/2)/v*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-1/6/v*(-3/v*(-2*v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)-4*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v^2*c^4+12*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v^2*c^2+(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*v^6-2*(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2)*c^2*v^4+6*c^2*3^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*v^2-12*c^2*3^(1/2)*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)/(1/v*(v^3*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)+2*v*((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3)*c^2+((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(2/3)-11*v^2*c^4+12*v^2*c^2+v^6-2*c^2*v^4)/((-15*v^4*c^4-37*v^2*c^6+18*c^2*v^4-18*v^2*c^4+54*c^4+v^8-3*v^6*c^2+6*c^3*(-3*v^6+96*c^2*v^4-111*v^2*c^4+6*v^4-54*v^2*c^2+81*c^2-3*v^10+6*v^8*c^2+51*c^4*v^6+6*v^8-66*v^6*c^2+75*c^6*v^4-84*v^4*c^4)^(1/2))*v)^(1/3))^(1/2))^(1/2) ※※※※※※ 太极漩涡:一个让牛顿成为菜鸟、麦克斯韦成为废物、爱因斯坦成为骗子的终极理论! |
| 对【97楼】说:谢谢对本数学题的关注,慢慢来,应该可以解出n的范围… |
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对【100楼】说:自我感觉本数学题较难解(我也怕动脑筋),阁下的设V=aC代入方程(-1<a<1),除以c4,这应该是一种方法,此外,或许下面的思路能突破什么,但难点是解高次方程组,-8n3+21n2-16n+4>0只是一个方面… 未必成熟的本题解题构思 本题的题设是v<c,这个题设实际上隐含了v2<c2。因为题意是要找算式不为零结果的实数n的范围,所以,只要把使原算式为零的所有n找出来,去掉,剩余的n就是使原算式不为零的n了。根据这种题意,可以先设原算式为零,所以有 v4n4-2v4n3+v4n2-v2n2c2+2nc4-c4=0 上式实际上是关于v2的二次方程。把上式进一步化简,得 n2(n-1)2v4-v2n2c2+(2n-1)c4=0 要使上式成立,必要条件是v2在实数范围存在,v2存在的必要条件是判别式△≥0,所以,n2(-8n3+21n2-16n+4)≥0①。 当n≠0且n≠1时,v2=(n2±△1/2)c2/2 n2(n-1)2, 因为v2不为负,所以必有n2≥△1/2②。 注意到题设条件v<c,推及v2<c2,所以,由v2=(n2±△1/2)c2/2 n2(n-1)2 便得到: (n2±△1/2)/2 n2(n-1)2<1③。 到此,本题的解便归结为下述高次不等式组的解: n2(-8n3+21n2-16n+4)≥0①; n2≥[n2(-8n3+21n2-16n+4)]1/2②; (n2±[n2(-8n3+21n2-16n+4)]1/2)/2 n2(n-1)2<1③。 往下的工作就是解高次不等式组,找出公共解n,去掉,剩余的n就是符合原题要求的n了。 如果上述构思没有问题的话,下面,这就要看“高次不等式组”高手们的了(我对“高次不等式组”却不内行)… 如果公共解n不存在,那就是任意实数都能使原算式不为零,这时,对应的物理意义就是:相对论的“同时相对性”结论在任意实数范围都不成立!!… |
| TO[102楼]:谢谢老朋友的惦念,我的手机15885756611,不过,没有预约一般都可能错过会晤时间(我的同学几次到我那里都没找到我)… |
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讲述一下这样的解题技巧﹕ 1.首先将方程化解为第[97楼]的形式,得到根号内有根号的等式就在很大程度上限止了n的取值范围,再找出满足0<a2<1的条件就是本方程的解。 2.在根号内的根号中是一个n的三次函数,先建立y=f(x)的直角坐标作草图(数学基础好的不用作图),便可发现是有两个拐点的∽曲线,经第二个拐点后函数快速下滑,而根据题意y又必须取大于或等于零,所以我们用求导数的方法很容易找到两个拐点(我的[103楼]没计算),再求y等于零的n极大值。 3.求解y=0的方程解可以用代数法,先将方程化为x3+bx+c=0的形式,但代数法公式难记,不如根据图示直接在电脑上用数值逼近法快,得到本函数唯一的一个实数根是 n≤1.53329641666031,此曲线与x(n)轴只有一个交点。 4.确定根号内根号的正负取值,先取正号用数值代入无解,再取负号代入只有0.5<n<1符合题意。 ※※※※※※ 相对论误导科学走邪路,是非曲折待历史见证;引力场以太旧貌焕新颜,定海神柱将扭转乾坤。.................... 想当初时空迷思闯科海,荣辱以乐可生命当歌;看如今闲庭信步攀高峰,重构宇宙再平展时空。 |
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利用Matlab的绘图功能,我求出来了。 根据97楼,首先可以看出n>0,n不等于1. 根据-8n^3+21n^2-16n+4>0得出n<1.5333(求出的根)图1. 在以上范围内,图2得出0.5<n<1.5333,图3还是上述结论。 图4得出最终范围:0.5<n<1.这是正负两个根的结论。 同理,另两个根无解,因为根据最终表达式使a超出【-1,1】的范围。
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>> syms a n
>> solve('a^4*n^4-2*a^4*n^3+a^4*n^2-a^2*n^2+2*n-1=0',a) ans = 1/(2*n+2*n^3-4*n^2)*2^(1/2)*(n*(1+n^2-2*n)*(n+(21*n^2-16*n+4-8*n^3)^(1/2)))^(1/2) -1/(2*n+2*n^3-4*n^2)*2^(1/2)*(n*(1+n^2-2*n)*(n+(21*n^2-16*n+4-8*n^3)^(1/2)))^(1/2) 1/(2*n+2*n^3-4*n^2)*2^(1/2)*(n*(1+n^2-2*n)*(n-(21*n^2-16*n+4-8*n^3)^(1/2)))^(1/2) -1/(2*n+2*n^3-4*n^2)*2^(1/2)*(n*(1+n^2-2*n)*(n-(21*n^2-16*n+4-8*n^3)^(1/2)))^(1/2) >> eval('n=0.6') n = 0.6000 >> eval(ans) ans = 2.3735 -2.3735 0.7851 -0.7851 把n=0.6代入的结果。四个a值。有个V=0.7851C,楼主你可能要失望了! ※※※※※※ 天地之道,以阴阳二气造化万物。是故易有太极,是生两仪。两仪生四象,四象生八卦。 |
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对【110楼】说: 这些图与我的分步计算结果完全一致,怎么虚数部分还会有线段出现? ※※※※※※ 相对论误导科学走邪路,是非曲折待历史见证;引力场以太旧貌焕新颜,定海神柱将扭转乾坤。.................... 想当初时空迷思闯科海,荣辱以乐可生命当歌;看如今闲庭信步攀高峰,重构宇宙再平展时空。 |