用Mathematica求解方程组

四个方程加一个约束条件一共五个等式#mathematica##方程组#构成一个方程组，求解3个未知数，alpha、beta、gamma，得不出来结果，求大神帮助！
v1 = Solve[{2 ep[1] c[1]/(c[1]^2 - x) == \[Alpha]*
c[1]/(c[1]^2 - x) + \[Beta]*c[1] + \[Gamma]/c[1],
2 ep[2] c[2]/(c[2]^2 - x) == \[Alpha]*c[2]/(c[2]^2 - x) + \[Beta]*
c[2] + \[Gamma]/c[2],
2 ep[3] c[3]/(c[3]^2 - x) == \[Alpha]*c[3]/(c[3]^2 - x) + \[Beta]*
c[3] + \[Gamma]/c[3],
2 ep[4] c[4]/(c[4]^2 - x) == \[Alpha]*c[4]/(c[4]^2 - x) + \[Beta]*
c[4] + \[Gamma]/
c[4], (-c[1]^2 (c[2]^2 - c[3]^2) ep[1] +
c[2]^2 (c[1]^2 - c[3]^2) ep[2] -
c[3]^2 (c[1]^2 - c[2]^2) ep[3]) c[
4]^4 + (c[1]^2 (c[2]^4 - c[3]^4) ep[1] -
c[2]^2 (c[1]^4 - c[3]^4) ep[2] +
c[3]^2 (c[1]^4 - c[2]^4) ep[
3] + (c[1]^2 - c[2]^2) (c[1]^2 - c[3]^2) (c[2]^2 -
c[3]^2) ep[4]) c[4]^2 +
c[1]^2 c[2]^2 c[
3]^2 (-(c[2]^2 - c[3]^2) ep[1] + (c[1]^2 - c[3]^2) ep[
2] - (c[1]^2 - c[2]^2) ep[3]) ==
0}, {\[Alpha], \[Beta], \[Gamma]}]