X^2+2xy+y^2-X-y+1/4
答案:3 悬赏:30
解决时间 2021-11-28 13:21
- 提问者网友：全員惡人
- 2021-11-28 09:57
X^2+2xy+y^2-X-y+1/4
最佳答案
- 二级知识专家网友：堕落奶泡
- 2021-11-28 11:29
x^2+2xy+y^2-x-y+1/4
=(x+y)^2-(x+y)+1/4
=(x+y-1/2)^2
=(x+y)^2-(x+y)+1/4
=(x+y-1/2)^2
全部回答
- 1楼网友：修女的自白
- 2021-11-28 12:04
x^2+2xy+y^2=1............1
2x^2-y=2..............2
由2式得
(x+y)^2=1..........3
由2式得
y=2x^2-2..........4
将4式代入3式得
(x+2x^2-2)^2-1=0
(x+2x^2-2-1)(x+2x^2-2+1)=0
(2x^2+x-3)(2x^2+x-1)=0
(2x+3)(x-1)(2x^2+x-1)=0
(2x+3)(x-1)(2x-1)(x+1)=0
x1=-3/2
x2=1
x3=1/2
x4=-1
y1=2x^2-2=2*(-3/2)^2-2=5/2
y2=2x^2-2=2*1^2-2=0
y3=2x^2-2=2*(1/2)^2-2=-3/2
y2=2x^2-2=2*(-1)^2-2=0
所以：(x1=-3/2,y1=5/2),(x2=1,y2=0), (x3=1/2,y=-3/2),(x4=-1,y=0)
- 2楼网友：开心就好
- 2021-11-28 11:50
原式=(x+y)²-(x+y)+1/4]=(x+y-1/2)²
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