已知实数x,y满足2x²+6xy+9y²-2x+1=0,试求x,y的值.
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![已知实数x,y满足2x²+6xy+9y²-2x+1=0,试求x,y的值.](/uploads/image/z/591372-36-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B32x%26%23178%3B%2B6xy%2B9y%26%23178%3B-2x%2B1%3D0%2C%E8%AF%95%E6%B1%82x%2Cy%E7%9A%84%E5%80%BC.)
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