已知实数xy,满足10x²-2xy+y²+6x+1=0,求x+y

已知实数xy,满足10x²-2xy+y²+6x+1=0,求x+y
已知实数xy,满足10x²-2xy+y²+6x+1=0,求x+y

已知实数xy,满足10x²-2xy+y²+6x+1=0,求x+y
10x²-2xy+y²+6x+1=0
（3x+1）²＋(x-y)²=0
3x+1=0
x-y=0
所以
x=y=-1/3
x+y=-2/3

10x^2-2xy+y^2+6x+1
=x^2-2xy+y^2+9x^2+6x+1
=(x-y)^2+(3x+1)^2=0
得x=y x=-1/3
所以x+y=-2/3

　　10x2-2xy+y2+6x+1=(x-y)2+(3x+1)2=0,当且仅当x-y=0,3x+1=0时等式成立，故x=y=-1/3,所以x+y=-2/3