Question

已知x+y=3,xy=1,a+b=5,ab=3,m=ax+by,n=bx+ay,求m^2n^2的值

Answer 1

因为x+y=3,xy=1,所以x^2+y^2=(x+y)^2-2xy=3^2-2*1=7.

同样,因为a+b=5,ab=3,所以a^2+b^2=19

于是mn=(ax+by)(bx+ay)=abx^2+a^2xy+b^2xy+aby^2

=ab(x^2+y^2)+(a^2+b^2)xy

=3*7+19*1=40

所以m^2n^2=1600