已知xyz≠0,且x y z满足 3x-4y-z=0 2x+y-8z=0 （求X²+Y²+Z²）/2xy+xz-2yz

题目

已知xyz≠0,且x y z满足 3x-4y-z=0 2x+y-8z=0 （求X²+Y²+Z²）/2xy+xz-2yz

答案

3x-4y-z=0 (1) 2x+y-8z=0 (2)
(1) +(2)*4
11x=33z
x=3z y=2z 代入
x^2+y^2+z^2/2xy+zx-2yz
=(3z)^2+(2z)^2+z^2/2*3z*2z+3z*z-2*2z*z
=14z^2/11z^2
=14/11