设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=
问题描述:
设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=
答
化简:m^2*n^2+8mn+16+m^2+n^2+2mn=0,
(mn+4)^2+(m+n)^2=0,
mn=-4,m=-n,
则当m=2时,n=-2,
当m=-2时,n=2.