已知4x-3y-6z=0,x+2y-7z=0,xyz不等于0,求xy+2yz+xz分之2x^2+3y^2+6z^2

题目

已知4x-3y-6z=0,x+2y-7z=0,xyz不等于0,求xy+2yz+xz分之2x^2+3y^2+6z^2

答案

4x-3y-6z=0, (1)
x+2y-7z=0, (2)
(2)×4-(1)得：
11y=22z
y=2z
代入(2)得：
x=7z-4z
x=3z
xy+2yz+xz分之2x^2+3y^2+6z^2
=(18z²+12z²+6z²)/(6z²+4z²+3z²)
=36/13