Question

已知关于x的方程m的平方x的平方+(4-4m)x+4=0

Answer 1

m^2x^2+(4-4m)x+4=0

|x1|=|x2|

(1)x1=-x2,即有x1+x2=0

即有x1+x2=-(4-4m)/m^2=0

m=1

代入得到x^2+4=0,方程无解,故舍.

(2)x1=x2,即方程有二个相等的根,则有判别式=0

即有:(4-4m)^2-16m^2=0

16-32m+16m^2-16m^2=0

m=1/2