X²-8X+Y²-6Y+25=0 求X+Y的值

X²-8X+Y²-6Y+25=0 求X+Y的值
X²-8X+Y²-6Y+25=0 求X+Y的值

X²-8X+Y²-6Y+25=0 求X+Y的值
X²-8X+Y²-6Y+25=0
x^2-8x+16+y^2-6y+9=0,
(x^2-8x+16)+(y^2-6y+9)=0
(x-4)^2+(y-3)^2=0
所以x-4=0,y-3=0,
解得x=4,y=3
所以x+y=7

配方：（X-4）^2+(Y-3)^2=0
所以X=4，Y=3

X²-8X+Y²-6Y+25=0
X²-8X+9+Y²-6Y+16=0
（x-4）^2+（x-3）^2=0
所以
x=4，y=3（平方大于零）
x+y=7