Question

x^2(x-1)^2-32(x^2-x)+60=0

Answer 1

令a=x^2-x

则x^2(x-1)^2=[x(x-1)]^2=(x^2-x)^2=a^2

所以a^2-32a+60=0

(a-2)(a-30)=0

a=2,a=30

x^2-x=a=2

x^2-x-2=0

(x-2)(x+1)=0

x=2,x=-1

x^2-x=a=30

x^2-x-30=0

(x-6)(x+5)=0

x=6,x=-5

所以有四解

x=2,x=-1,x=6,x=-5