已知：m²=n+2,n²=m+2（m≠n）．求：m³+2mn+n³的值．急,如题.

已知：m²=n+2,n²=m+2（m≠n）．求：m³+2mn+n³的值．急,
如题.

m²=n+2
n²=m+2
两式相减得
m²-n²=n-m
(m-n)(m+n)=-(m-n)
因为m-n不等于0,两边同时除以(m-n)
m+n=-1
m³-2mn+n³
=m³-mn+n³-mn
=m(m²-n)+n(n²-m)
=2m+2n
=2(m+n)
=-2