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

题目

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

答案

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