(注:m²=n+2 n²=m+2 (n≠m) 求m³—2mn+n³
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(注:m²=n+2 n²=m+2 (n≠m) 求m³—2mn+n³
(注:m²=n+2 n²=m+2 (n≠m) 求m³—2mn+n³
(注:m²=n+2 n²=m+2 (n≠m) 求m³—2mn+n³
m³—2mn+n³=m³- mn+n³-mn=m(m²-n)+n(n²-m)
=m(n+2-n)+n(m+2-m)
=2m+2n
由m²=n+2,n²=m+2 得 m²-n=2,n²-m=2
所以m²-n=n²-m
即m²-n²-n+m=0
(m-n)(m+n+1)=0
又因为n≠m,所以m+n+1=0
即m+n=-1
所以原式=-2
由m²=n+2, n²=m+2 分别得出: m²-n=2, n²-m=2
m²- n²=(m-n)(m+n)=n-m,n≠m,所以m+n=-1
m³—2mn+n³=m(m²-n)+n( n²-m)
=2m+2n
=2(m+n)
=-2
因为m²=n+2, n²=m+2 得 m²-n=2,n²-m=2
m²- n²=(m-n)(m+n)
m²- n²=n+2-m-2=n-m,因为n≠m,所以m+n=-1
m³—2mn+n³=m(m²-n)+n( n²-m)
=2m+2n
=2(m+n)
=-2