已知3x-4y-z=0 2x+y-8z =0,求(x²+y²-z²)/(xy+yz)的值

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已知3x-4y-z=0 2x+y-8z =0,求(x²+y²-z²)/(xy+yz)的值
已知3x-4y-z=0 2x+y-8z =0,求(x²+y²-z²)/(xy+yz)的值

已知3x-4y-z=0 2x+y-8z =0,求(x²+y²-z²)/(xy+yz)的值
6x-8y-2z=0
6x+3y-24z=0
11y-22z=0
y=2z
3x-4(2z)-z=0
x=3z
(x²+y²-z²)/(xy+yz)=[(3z)^2+(2z)^2-z^2]/[(3z)+z](2z)=3/2

由3x-4y-z=0得z=3x-4y ③
由2x+y-8z=0得y=8z-2x ④
④代入③得
x=3z
y=2z
将x=3z,y=2z代入得
(x²+y²-z²)/(xy+yz)
=(9z²+4z²-z²)/(6z²+2z²)
=12z²/8z²
=12/8
=3/2

知3x-4y-z=0
2x+y-8z =0,
把z看成已知数，解得x=3z，y=2z
求(x²+y²-z²)/(xy+yz)的值
代入则
= (9z²+4z²-z²)/ (6z²+2z²)
= 12 / 8
= 3/2x和y是怎么具体得出的，可以再详细点...

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知3x-4y-z=0
2x+y-8z =0,
把z看成已知数，解得x=3z，y=2z
求(x²+y²-z²)/(xy+yz)的值
代入则
= (9z²+4z²-z²)/ (6z²+2z²)
= 12 / 8
= 3/2

收起

用一个字母表示另外两个字母。
3X-4Y=Z
2X+Y=8Z，
解得：X=3Z，Y=2Z，
∴(x²+y²-z²)/(xy+yz)
=(9Z²+4Z²-z²)/(6Z²+2z²)
=12/8
=3/2。

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