5 x 的平方－3x y＋二分之一y的平方－2 x ＋二分之一y＋四分之一等于0
5x^2-3xy+y^2/2-2x+y/2+1/4=0
20x²-12xy+2y²-8x+2y+1=0
20x²-12xy+y²+y²-8x+2y+1=0
(2x-y)(10x-y)+y²-4(2x-y)-2y+1=0
(2x-y)(10x-y-4)+(y-1)²=0
(2x-y)[5(2x-y)+4y-4]+(y-1)²=0
5(2x-y)² +4(2x-y)(y-1)+(y-1)²=0
假設(shè) a=2x-y,b=y-1,代入上式,
即 5a²+4ab+b²=0
4a²+4ab+b²+a²=0
(2a+b)²+a²=0
所以 a=0
2x-y=0
y=2x
2a+b=0
2(2x-y)+(y-1)=0
4x-y-1=0,
代入y=2x,
2x-1=0
x=1/2
y=1
xy=1/2