已知5x^2-3xy+1/2y^2-2x+1/2y+1/4=0 求x,y的值

题目

已知5x^2-3xy+1/2y^2-2x+1/2y+1/4=0 求x,y的值

答案

5x^2-3xy+1/2y^2-2x+1/2y+1/4=0
乘以4通分之后得到：
20x^2-12xy+2y^2-8x+2y+1=0
（4x-y)^2+(2x-y)^2-2(4x-y)+1=0
(4x-y-1)^2+(2x-y)^2=0
得 4x-y-1＝0
2x-y＝0
解得：x=1/2 ,y=1