已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3
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已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3已知m^2=n+2,n^2=m+2(m≠n),求m^3-2m
已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3
已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3
已知m^2=n+2,n^2=m+2(m≠n),求m^3-2mn+n^3
m^2 -n^2 = n-m
(m+n)(m-n) =n-m
m+n = -1
m^3 = m^2 * m = mn +2m
n^3 =mn +2n
m^3-2mn+n^3 =2m+2n = -2
m^3-2mn+n^3
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2m+2n
m^2=n+2
n^2=m+2
两式相减得:m^2-n^2 = n-m
(m+n)(m-n) = -(m-n)
m≠n,∴m-n≠0
∴m+n = -1
∵m^2=n+2,∴m^3 = m(n+2) = mn+2m
∵n^2=m+2,∴n^3 = n(m+2) = mn+2m
∴m^3-2mn+n^3 = mn+2m - 2mn + mn+2m = 2(m+n) = 2*(-1) = -2
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