Question

已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.

Answer 1

4|m+n|+4m^2+1=4m

即4|m+n| +4m^2-4m+1=0

4|m+n|+(2m-1)^2=0

根据非负数的性质：

m+n=0

2m-1=0

即m=1/2,n=-1/2

(m-n)^2=[1/2-(-1/2)]^2=1