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

(x+3y)^2+(x-1)^2=0
x=1
y=-1/3

2x^2+6xy+9y^2-2x+1=0
x^2+6xy+9y^2+x^2-2x+1=0
(x+3y)^2+(x-1)^2=0
∵(x+3y)^2≥0,(x-1)^2≥0
∴x+3y=0,x-1=0
x=1,y=-1/3