已知:m²=n+2,n²=m+2(m≠n).求:m³+2mn+n³的值.急,如题.
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![已知:m²=n+2,n²=m+2(m≠n).求:m³+2mn+n³的值.急,如题.](/uploads/image/z/4032049-49-9.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9Am%26%23178%3B%3Dn%2B2%2Cn%26%23178%3B%3Dm%2B2%EF%BC%88m%E2%89%A0n%EF%BC%89%EF%BC%8E%E6%B1%82%EF%BC%9Am%26%23179%3B%2B2mn%2Bn%26%23179%3B%E7%9A%84%E5%80%BC%EF%BC%8E%E6%80%A5%2C%E5%A6%82%E9%A2%98.)
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.
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