Question

已知(x+my)(x+ny)=x的平方+2xy减8y的平方,求mn(m+n)的值

Answer 1

(x+my)(x+ny)=x^2+2xy-8y^2

(x+my)(x+ny)

=x^2+(m+n)xy+mny^2

=x^2+2xy-8y^2

根据对应项系数相等,得

m+n=2

mn=-8

解得

m=4

n=-2

mn(m+n)=-8×2=-16