题目

已知x/2=y/3=z/4,则(x^2-2y^2+3z^2)/(xy+2yz+3xz)的值是
为什么可以令x/2=y/3=z/4=t
等于x=2t,y=3t,z=4t

提问时间：2020-11-26

答案

因为 x/2=y/3=z/4 知道 x :y :z = 2 :3 :4
所以
令x/2=y/3=z/4=t
则x=2t,y=3t,z=4t
(x^2-2y^2+3z^2)/(xy+2yz+3xz)
=(4t^2-18t^2+48t^2)/(6t^2+24t^2+24t^2)
=34t^2/54t^2
=34/54
=17/27