(1)已知6x^2+xy-12y^2=0(xy不等于0),求x/y的值(2)已知(x^2+y^2)(x^2+y^2+2)-15=0,求x^2+y^2的值(3)已知(x^2+y^2-1)(x^2+y^2+2)-18=0,求x^2+y^2的值(4)若6x^2-xy-15y^2=0,求x^2-6xy+5y^2/x^2-4xy-5y^2的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 11:52:11
![(1)已知6x^2+xy-12y^2=0(xy不等于0),求x/y的值(2)已知(x^2+y^2)(x^2+y^2+2)-15=0,求x^2+y^2的值(3)已知(x^2+y^2-1)(x^2+y^2+2)-18=0,求x^2+y^2的值(4)若6x^2-xy-15y^2=0,求x^2-6xy+5y^2/x^2-4xy-5y^2的值](/uploads/image/z/8636918-14-8.jpg?t=%EF%BC%881%EF%BC%89%E5%B7%B2%E7%9F%A56x%5E2%2Bxy-12y%5E2%3D0%28xy%E4%B8%8D%E7%AD%89%E4%BA%8E0%29%2C%E6%B1%82x%2Fy%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E5%B7%B2%E7%9F%A5%28x%5E2%2By%5E2%29%28x%5E2%2By%5E2%2B2%29-15%3D0%2C%E6%B1%82x%5E2%2By%5E2%E7%9A%84%E5%80%BC%EF%BC%883%EF%BC%89%E5%B7%B2%E7%9F%A5%EF%BC%88x%5E2%2By%5E2-1%29%28x%5E2%2By%5E2%2B2%29-18%3D0%2C%E6%B1%82x%5E2%2By%5E2%E7%9A%84%E5%80%BC%EF%BC%884%EF%BC%89%E8%8B%A56x%5E2-xy-15y%5E2%3D0%2C%E6%B1%82x%5E2-6xy%2B5y%5E2%2Fx%5E2-4xy-5y%5E2%E7%9A%84%E5%80%BC)
(1)已知6x^2+xy-12y^2=0(xy不等于0),求x/y的值(2)已知(x^2+y^2)(x^2+y^2+2)-15=0,求x^2+y^2的值(3)已知(x^2+y^2-1)(x^2+y^2+2)-18=0,求x^2+y^2的值(4)若6x^2-xy-15y^2=0,求x^2-6xy+5y^2/x^2-4xy-5y^2的值
(1)已知6x^2+xy-12y^2=0(xy不等于0),求x/y的值
(2)已知(x^2+y^2)(x^2+y^2+2)-15=0,求x^2+y^2的值
(3)已知(x^2+y^2-1)(x^2+y^2+2)-18=0,求x^2+y^2的值
(4)若6x^2-xy-15y^2=0,求x^2-6xy+5y^2/x^2-4xy-5y^2的值
(1)已知6x^2+xy-12y^2=0(xy不等于0),求x/y的值(2)已知(x^2+y^2)(x^2+y^2+2)-15=0,求x^2+y^2的值(3)已知(x^2+y^2-1)(x^2+y^2+2)-18=0,求x^2+y^2的值(4)若6x^2-xy-15y^2=0,求x^2-6xy+5y^2/x^2-4xy-5y^2的值
1.方程等号两边同除以y^2得:6*(x/y)^2+(x/y)-12=0
解此二次方程得x/y=4/3或-3/2
2.令x^2+y^2=t则原方程为t(t+2)-15=0
解得t=3或-5
又因为x^2+y^2必为非负数所以x^2+y^2=3
3.同样的方法,设t再求二次方程,得t=4或-5
又因为x^2+y^2必为非负数所以x^2+y^2=4
4.此题同1中的方法求得x/y=5/3或-3/2
再令x^2-6xy+5y^2/x^2-4xy-5y^2分子分母同除以y^2得
(x/y)^2-6x/y+5/(x/y)^2-4x/y-5
代入x/y=5/3或-3/2得
原式=1/4或5
方程等号两边同除以y^2得:6*(x/y)^2+(x/y)-12=0
解此二次方程得x/y=4/3或-3/2
1:x/y= - 3/2或者4/3
2:x^2+y^2=3
3:x^2+y^2=4
4:x^2-6xy+5y^2/x^2-4xy-5y^2=1/4或5
(1)
6x^2+xy-12y^2=0
(2x+3y)(3x-4y) =0
x = -3y/2 or x = 4y/3
x/y = -3/2 or x/y= 4/3
(2)
(x^2+y^2)(x^2+y^2+2)-15=0
(x^2+y^2)^2 +2(x^2+y^2)-15=0
(x^2+y^2+5)(x^2+y^2-3)...
全部展开
(1)
6x^2+xy-12y^2=0
(2x+3y)(3x-4y) =0
x = -3y/2 or x = 4y/3
x/y = -3/2 or x/y= 4/3
(2)
(x^2+y^2)(x^2+y^2+2)-15=0
(x^2+y^2)^2 +2(x^2+y^2)-15=0
(x^2+y^2+5)(x^2+y^2-3)=0
x^2+y^2= -5 or x^2+y^2=3
(3)
(x^2+y^2-1)(x^2+y^2+2)-18=0
(x^2+y^2)^2+(x^2+y^2)-20 =0
((x^2+y^2)-4)((x^2+y^2)+5) =0
x^2+y^2 = 4 or x^2+y^2=-5
(4)
6x^2-xy-15y^2=0
收起