已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n

已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n
已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n

已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n
解
2m²+2mn+n²+2m+1=0
(m²+2mn+n)+(m²+2m+1)=0
(m+n)²+(m+1)²=0
∵(m+n)²>=0
(m+1)²>=0
∴m+n=0
m+1=0
∴m=-1,n=1
∴(m²+n²)x=m-n
2x=(-1-1)
2x=-2
∴x=-1

2m²+2mn+n²+2m+1=0, m²+2mn+n²+m²+2m+1=0, (m+n)²+(m+1)²=0
m=-n m=-1 m=-1 n=1
(m²+n²)x=m-n 2x=-2 x=-1