程组x²-2xy+x+3=0,4xy-6x²+x-2y+4=0 方程组√(x+y)-√(x+9/y)=2,2x+y+9/y=10
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/28 23:17:23
![程组x²-2xy+x+3=0,4xy-6x²+x-2y+4=0 方程组√(x+y)-√(x+9/y)=2,2x+y+9/y=10](/uploads/image/z/1614741-69-1.jpg?t=%E7%A8%8B%E7%BB%84x%26%23178%3B-2xy%2Bx%2B3%3D0%2C4xy-6x%26%23178%3B%2Bx-2y%2B4%3D0+%E6%96%B9%E7%A8%8B%E7%BB%84%E2%88%9A%28x%2By%29-%E2%88%9A%28x%2B9%2Fy%29%3D2%2C2x%2By%2B9%2Fy%3D10)
程组x²-2xy+x+3=0,4xy-6x²+x-2y+4=0 方程组√(x+y)-√(x+9/y)=2,2x+y+9/y=10
程组x²-2xy+x+3=0,4xy-6x²+x-2y+4=0 方程组√(x+y)-√(x+9/y)=2,2x+y+9/y=10
程组x²-2xy+x+3=0,4xy-6x²+x-2y+4=0 方程组√(x+y)-√(x+9/y)=2,2x+y+9/y=10
x²-2xy+x+3=0,1)
4xy-6x²+x-2y+4=0 2)
1)*2+2):-4x^2+3x+10-2y=0
得:y=-2x^2+1.5x+5 3)
代入1):x^2+4x^3-3x^2-10x+x+3=0
4x^3-2x^2-9x+3=0
这比较坑了,居然不能进行有理分解.是不是题目抄错了?
只能用求根公式解为:
x1=1.60879035465433
x2=-1.43390798834357
x3=0.325117633689237
代入3)即可算得y1,y2,y3
y1=2.2367727215239
y2=-1.2630462205864
y3=5.2762734990625
√(x+y)-√(x+9/y)=2,
2x+y+9/y=10
记a= √(x+y)>=0,b= √(x+9/y)>=0
则方程组化为:
a-b=2 1)
a^2+b^2=10 2)
1)式平方-2式得:-2ab=-6,得:ab=3 3)
2)+3)*2得:(a+b)^2=16,故有a+b=4或-4 4)
由1),4),解得:a=3,b=1,或a=-1,b=-3(负根,舍去)
a=3,b=1时,有x+y=9,x+9/y=1,解得:x=0,y=9 或x=10,y= -1
因此原方程组有2组(0,9),(10,-1)