已知m^2+n^2-6m+10n+34=0,求m-n

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 03:46:14
已知m^2+n^2-6m+10n+34=0,求m-n

已知m^2+n^2-6m+10n+34=0,求m-n
已知m^2+n^2-6m+10n+34=0,求m-n

已知m^2+n^2-6m+10n+34=0,求m-n
原式=(m^2-6m+9)+(n^2+10n+25)
=(m-3)^2+(n+5)^2
m=3
n=-5
m-n=8
努力学习吧

m²-6m+9+n²+10n+25=0
(m-3)²+(n+5)²=0
则:m-3=0,n+5=0
得:m=3,n=-5
所以,m-n=8
祝你开心!希望能帮到你,如果不懂,请追问,祝学习进步!O(∩_∩)O

m^2+n^2-6m+10n+34=0
(m²-6m+9)+(n²+10n+25)=0
(m-3)²+(n+5)²=0
∵(m-3)²≥0,(n+5)²≥0
∴m-3=0,n+5=0
∴m=3,n=-5
m-n=3-(-5)=8