已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.

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已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.4|m+n|+4m^

已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.
已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.

已知4|m+n|+4m^2+1=4m,求根号(m-n)^2.
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

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

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

4|m+n|+4m^2+1=4m
解原式可化为
4|m+n|+4m^2+1-4m=0
∴4|m+n|+(2m-1)^2=0
∵4|m+n|≥0,(2m-1)^2≥0
∴m+n=0,2m-1=0
m=1/2,n=-1/2
∴√(m-n)^2=√1=1