解方程组:{x(x+y+z)=6 {y(x+y+z)=9 {z(x+y+z)=10
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解方程组:{x(x+y+z)=6 {y(x+y+z)=9 {z(x+y+z)=10
![解方程组:{x(x+y+z)=6 {y(x+y+z)=9 {z(x+y+z)=10](/uploads/image/z/17150776-16-6.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B%E7%BB%84%EF%BC%9A%7Bx%28x%2By%2Bz%29%3D6+%7By%28x%2By%2Bz%29%3D9+%7Bz%28x%2By%2Bz%29%3D10)
设x+y+z≠0
则
x(x+y+z)=6 (1)
y(x+y+z)=9 (2)
z(x+y+z)=10 (3)
(1)/(2)得:x/y=2/3
(3)/(1)得:z/x=5/3
(2)/(3)得:y/z=9/10
x=2/3y,z=10/9y
代入(1)得
y(2/3y+y+10/9y)=9
y=±9/5
当y=9/5时,x=6/5,z=2
当y=-9/5时,x=-6/5,z=-2
则
x(x+y+z)=6 (1)
y(x+y+z)=9 (2)
z(x+y+z)=10 (3)
(1)/(2)得:x/y=2/3
(3)/(1)得:z/x=5/3
(2)/(3)得:y/z=9/10
x=2/3y,z=10/9y
代入(1)得
y(2/3y+y+10/9y)=9
y=±9/5
当y=9/5时,x=6/5,z=2
当y=-9/5时,x=-6/5,z=-2
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