Question

（x+2y+2m)(2x-y+n)=2x^2+3xy-2y^2+5y-2 求m、n的值！

（x+2y+2m)(2x-y+n)=2x^2+3xy-2y^2+5y-2 求m、n的值！

Answer 1

（x+2y+2m)(2x-y+n)
=2x^2-xy+nx+4xy-2y^2+2ny+4mx-2my+2mn
=2x^2+3xy-2y^2+(4m+n)x-(2m-2n)y+2mn
=2x^2+3xy-2y^2+5y-2
所以4m+n=0且2m-2n=-5且2mn=-2
所以m=-1/2,n=2.

Answer 2

原式为一恒等式,将左式展开,多项式对应项系数相等即可.左式展开得2x^2+3xy-2y^2+(4m+n)x+(2n-2m)y+2mn
得到方程组4m+n=0 , 2n-2m=5 , 2mn=-2
解得m=-1/2 n=2