m^2+n^2-6m+10n+34=0,求m+n

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m^2+n^2-6m+10n+34=0,求m+nm^2+n^2-6m+10n+34=0,求m+nm^2+n^2-6m+10n+34=0,求m+nm²-6m+9+n²+10n+25=

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

m^2+n^2-6m+10n+34=0,求m+n
m²-6m+9+n²+10n+25=（m-3）²+（n+5）²=0
所以m=3,n=-5
m+n=3-5=-2

由条件式
m^2+n^2-6m+10n+34=0
→
(m^2-6m+9)+(n^2+10n+25)=0
→
(m-3)^2+(n+5)^2=0
由平方非负性
m=3
n=-5
∴
m+n=-2

m^2+n^2-6m+10n+34=0
(m^2-6m+9)+(n^2+10n+25)=0
(m-3)^2+(n+5)^2=0
m=3 n=-5
m+n=3-5=-2

m^2+n^2-6m+10n+34=0
（m^2-6m）+(n^2+10n)+34=0
(m-3)^2+(n+5)^2-9-25+34=0
(m-3)^2+(n+5)^2=0
得m=3
n=-5

34=9+25
所以(m²-6m+9)+(n²+10n+25)=0
(m-3)²+(n+5)²=0
平方大于等于0，相加等于0
若有一个大于0，则另一个小于0，不成立。
所以两个都等于0
所以m-3=0,n+5=0
m=3,n=-5
m+n=-2

（m-3）^2+（n+5）^2=0.则m＝3,n＝-5.所以m＋n＝-2.

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