已知实数x,y满足x2+y2-xy+x-1/2y+1/4=0 试求x,y的值

已知实数x,y满足x2+y2-xy+x-1/2y+1/4=0 试求x,y的值
已知实数x,y满足x2+y2-xy+x-1/2y+1/4=0 试求x,y的值

已知实数x,y满足x2+y2-xy+x-1/2y+1/4=0 试求x,y的值
x²+y²-xy+x -y/2 +1/4=0
4x²+4y²-4xy+4x-2y+1=0
4x²-4xy+y²+2(2x-y) +1+3y²=0
(2x-y)²+2(2x-y)+1 +3y²=0
(2x-y+1)²+3y²=0
平方项恒非负,两平方项之和=0,两平方项分别=0
2x-y+1=0 (1)
y=0 (2)
y=0代入(1)
2x=y-1=0-1=-1 x=-1/2
x=-1/2 y=0

凑成完全平方：x²+y²-xy+x -y/2 +1/4=0
4x²+4y²-4xy+4x-2y+1=0
4x²-4xy+y²+2(2x-y) +1+3y²=0
(2x-y)²+2(2x-y)+1 +3y²=0
(2x-y+1)²+3y²=0
所以：2x-y+1=0 y=0
即x=-1/2
y=0