设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/29 13:50:11
设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m=,n=设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m=,n=设实数m,n满足m^2*n^2+m^2+

设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=
设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=

设实数m,n满足m^2*n^2+m^2+n^2+10mn+16=0,则m= ,n=
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.

原式变形为:(mn+4)^2+(m+n)^2=0
则得到mn=-4,m+n=0 则得到m=2,n=-2或m=-2 ,n=2

m^2*n^2+m^2+n^2+10mn+16=(m^2+n^2+2mn)+(m^2*n^2+8mn+16)=(m+n)^2+(mn+4)^2=0
所以m+n=0且mn+4=0
{m=2,n=-2}或者{m=-2,n=2}
呵呵,这题只要合理分解就行了……

原式可化为:
(mn+4)^2+(m+n)^2=0
则 mn=-4,m+n=0;
顾 m=2 ,n=-2 或对调值