2x-y+z=0 3x+8y-z=0 且xyz不等于0,求(2x²-xy+z²)/(2x²
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2x-y+z=0 3x+8y-z=0 且xyz不等于0,求(2x²-xy+z²)/(2x²+y²-z²)的值
2x-y+z=0
3x+8y-z=0
两式相加得 5x + 7y = 0
x/y = - 7/5
x = - 7/5 y 代入 2x - y+z = 0 得
- 14/5 y - y + z = 0
z/y = 19/5
(2x²-xy+z²)/(2x²+y²-z²)
分子分母同除以 y²
= [ 2(x/y)² - x/y + (z/y)² ] / [ 2(x/y)² + 1 - (z/y)² ]
= [ 2*49/25 + 7/5 + 19² /25] / [ 2*49/25 + 1 - 19²/25 ]
= - 247 / 119
3x+8y-z=0
两式相加得 5x + 7y = 0
x/y = - 7/5
x = - 7/5 y 代入 2x - y+z = 0 得
- 14/5 y - y + z = 0
z/y = 19/5
(2x²-xy+z²)/(2x²+y²-z²)
分子分母同除以 y²
= [ 2(x/y)² - x/y + (z/y)² ] / [ 2(x/y)² + 1 - (z/y)² ]
= [ 2*49/25 + 7/5 + 19² /25] / [ 2*49/25 + 1 - 19²/25 ]
= - 247 / 119
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