已知实数x,y满足:2x²+6xy+9y²-2x+1=0,试求x,y的值

已知实数x,y满足:2x²+6xy+9y²-2x+1=0,试求x,y的值
已知实数x,y满足:2x²+6xy+9y²-2x+1=0,试求x,y的值

已知实数x,y满足:2x²+6xy+9y²-2x+1=0,试求x,y的值
2x²+6xy+9y²-2x+1=0
x²+6xy+9y²+x²-2x+1=0
(x+3y)²+(x-1)²=0
因为(x+3y)²>=0,(x-1)²>=0
所以(x+3y)²=0,(x-1)²=0
即x=-3y,x=1
1=-3y
y=-1/3
所以x=1,y=-1/3

:2x²+6xy+9y²-2x+1=0
x²+6xy+9y²+x²-2x+1=0
(x-3Y)²+(x-1)²=0
∴x=1=0，x=1
x-3y=0，y=1/3x=1/3

2x²+6xy+9y²-2x+1=0
(x²+6xy+9y²)+(x²-2x+1）=0
（x-3y)²+(x-1)²=0
x-3y=0, x-1=0
x=1, y=1/3

(x+3y)2 +（x-1）2=0
X=1 y= -1/3