已知{3X-4y-z=0 2x+y-8z=0 ,求x(x^2+y^2+z^2)/(xy+yz+2zx)的值,请写出过程.

来源：学生作业学帮网编辑：学帮网时间：2024/05/06 05:31:36

用其中一个变量表示另外两个变量,然后代入那个式子,再化简约分.
由3x-4y-z=0得z=3x-4y
由2x+y-8z=0得y = 8z-2x = 8(3x-4y) -2x = 22x - 32y 即33y = 22x
于是y = 2x / 3,z = 3x - 4 * 2x / 3 = x / 3
不过我算的答案是x,不知道问题出在哪儿,或者答案不对.

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 ⑤
y=2z

将x,y代入
(x^2+y^2+z^2)/(xy+yz+2zx)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+6z^2)
=(14z^2)/(14z^2)
=1

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