已知m^2+n^2-10m+6n+34=0,求代数式2m+5n的值.

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已知m^2+n^2-10m+6n+34=0,求代数式2m+5n的值.

已知m^2+n^2-10m+6n+34=0,求代数式2m+5n的值.
已知m^2+n^2-10m+6n+34=0,求代数式2m+5n的值.

已知m^2+n^2-10m+6n+34=0,求代数式2m+5n的值.
m^2+n^2-10m+6n+34=0
(m^2-10m+25)+(n^2+6n+9)=0
(m-5)^2+(n+3)^2=0
根据一个数的平方必然大于或者等于0
所以m-5=0 n+3=0
m=5,n=-3
2m+5n=10-15=-5

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

m^2+n^2-10m+6n+34=0
(m^2-10m+25)+(n^2+6n+9)=0
(m-5)^2+(n+3)^2=0
m=5 n=-3
2m+5n=10-15=-5

(m-5)^2+(n+3)^2=0
m=5 n=-3
2m+5n=-5