已知m눀=n+3,n눀=m+3,且m≠n。

2024-11-17 16:36:23
推荐回答(2个)
回答1:

(1)两式相减,m²-n²=n-m
(m+n)(m-n)=n-m=-(m-n)
因m≠n,故m-n≠0,故可以约分得:m+n=-1
(2)m=
-(n+1)与m²=n+3联立方程消去m,求解n,再解出m,最后带入求值

回答2:

m²=n+3
n²=m+3
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)
=3m+3n
=3(m+n)
=-3