Question

x^2(x-1)^2+(1-k^2)(x-1)^2+2x=0的实数解个数

Answer 1

设y=x-1/2,则x=y+1/2,

x(x-1)=y^2-1/4,

原方程变为(y^2-1/4)^2+(1-k^2)(y-1/2)^2+2y+1=0,

y^4-(1/2)y^2+1/16+(1-k^2)(y^2-y+1/4)+2y+1=0,

整理得y^4+(1/2-k^2)y^2+(k^2+1)y+21/16-k^2/4=0,

用公式法,繁!