X+Y=3,XY=1,a+b=5,ab=3,且m=ax+bx,n=bx+ay,求m3+n3的值为什么

Question

X+Y=3,XY=1,a+b=5,ab=3,且m=ax+bx,n=bx+ay,求m3+n3的值
为什么

Answer 1

m是不是=ax+by?
如果是则
m+n=ax+ay+bx+by
=a(x+y)+b(x+y)
=(x+y)(a+b)
=15
mn=abx^2+a^2xy+b^2xy+aby^2
=ab(x^2+y^2)+xy(a^2+b^2)
=ab[(x+y)^2-2xy]+xy[(a+b)^2-2ab]
=3*(9-2)+1*(25-6)
=40
所以m^3+n^3=(m+n)(m^2+n^2-mn)
=(m+n)[(m+n)^2-3mn]
=15*(15^2-3*40)
=1575