解方程组{x²+2xy+y²=25,﹙x-y﹚²-3x+3y+2=0}希望能尽快答复
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 08:11:12
![解方程组{x²+2xy+y²=25,﹙x-y﹚²-3x+3y+2=0}希望能尽快答复](/uploads/image/z/1611746-26-6.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B%E7%BB%84%7Bx%26%23178%3B%EF%BC%8B2xy%2By%26%23178%3B%3D25%2C%EF%B9%99x%EF%BC%8Dy%EF%B9%9A%26%23178%3B%EF%BC%8D3x%2B3y%2B2%3D0%7D%E5%B8%8C%E6%9C%9B%E8%83%BD%E5%B0%BD%E5%BF%AB%E7%AD%94%E5%A4%8D)
解方程组{x²+2xy+y²=25,﹙x-y﹚²-3x+3y+2=0}希望能尽快答复
解方程组{x²+2xy+y²=25,﹙x-y﹚²-3x+3y+2=0}
希望能尽快答复
解方程组{x²+2xy+y²=25,﹙x-y﹚²-3x+3y+2=0}希望能尽快答复
x²+2xy+y²=25,即(x+y)²=25得x+y=±5
﹙x-y﹚²-3x+3y+2=0
(x-y)²-3(x-y)+2=0
(x-y-1)(x-y-2)=0
得x-y=1或x-y=2
所以原方程组可化为
x+y=5,x-y=1 解得x=3,y=2
x+y=5,x-y=2 解得x=3.5,y=1.5
x+y=-5,x-y=1 解得x=-2,y=-3
x+y=-5,x-y=2 解得x=-1.5,y=-3.5
x²+2xy+y²=25
(x+y)²=25
x+y=±5
y=-x±5
带入第二个方程可求出四组解
x=-2, y=-3
x=3, y=2
x=-1.5, y=-3.5
x=3.5, y=1.5