已知方程组2x-y+z=0和5x+8y-z=0,且xyz不等于0,求(2x^-xy+z^)/(2x^+y^-z^)的值
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已知方程组2x-y+z=0和5x+8y-z=0,且xyz不等于0,求(2x^-xy+z^)/(2x^+y^-z^)的值
![已知方程组2x-y+z=0和5x+8y-z=0,且xyz不等于0,求(2x^-xy+z^)/(2x^+y^-z^)的值](/uploads/image/z/791423-71-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8B%E7%BB%842x-y%2Bz%3D0%E5%92%8C5x%2B8y-z%3D0%2C%E4%B8%94xyz%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E6%B1%82%282x%5E-xy%2Bz%5E%29%2F%282x%5E%2By%5E-z%5E%29%E7%9A%84%E5%80%BC)
xyz不等于0,即x,y,z都不为0
①: 2x-y+z=0
②: 5x+8y-z=0
①+②得x=-y
用x替换y,先代入①式得z=-3x,则z²=9x²
再代入下式得
(2x²-xy+z²)/(2x²+y²-z²)=-2
①: 2x-y+z=0
②: 5x+8y-z=0
①+②得x=-y
用x替换y,先代入①式得z=-3x,则z²=9x²
再代入下式得
(2x²-xy+z²)/(2x²+y²-z²)=-2
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