已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n
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![已知2m²+2mn+n²+2m+1=0,试解方程(m²+n²)x=m-n](/uploads/image/z/4032006-6-6.jpg?t=%E5%B7%B2%E7%9F%A52m%26%23178%3B%2B2mn%2Bn%26%23178%3B%2B2m%2B1%3D0%2C%E8%AF%95%E8%A7%A3%E6%96%B9%E7%A8%8B%28m%26%23178%3B%2Bn%26%23178%3B%29x%3Dm-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