已知x+y=3,xy=1,a+b=5,ab=3,且m=ax+by,n=bx+ay 求m^3+n^3的值
问题描述：
已知x+y=3,xy=1,a+b=5,ab=3,且m=ax+by,n=bx+ay 求m^3+n^3的值
答
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)^2-3...