Question

已知:m的2次方=n+2,n的2次方=m+2(m不等于n) 求m的3次方-mn+n的3次方的值 各位帮帮忙,把过程写出来

Answer 1

m²=n+2..........①
n²=m+2.........②
①-②,得:
(m-n)(m+n)=n-m
m≠n,则同时除以m-n,得:
m+n=-1
平方,得:
m²+2mn+n²=1
①+②得:
m²+n²=m+n+4=-1+4=3
所以2mn=1-3=-2
mn=-1

m³-mn+n³
=(m+n)(m²-mn+n²)-mn
=(-1)*(3+1)+1
=-4+1
=-3

Answer 2

m^2=n+2,n^2=m+2
则m^2-n^2=n-m
(m+n)(m-n)=n-m
(m+n+1)(m-n)=0
m不等于n
所以m+n=-1

m^3-2mn+n^3
=mm^2-2mn+nn^2
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2(m+n)
=2*(-1)
=-2