x+3y+7z=0 2x+5y+11z=0,求(x^2+y^2+z^2)/(xy+2yz+3xz)
问题描述：
x+3y+7z=0 2x+5y+11z=0,求(x^2+y^2+z^2)/(xy+2yz+3xz)
答
x+3y+7z=0 2x+5y+11z=0
x=2z,y=-3z
z=0,x=y=0分式无意义
(x^2+y^2+z^2)/(xy+2yz+3xz),z≠0
=[(2z)^2+(-3z)^2+z^2]/[(-2z*3z-2*3z*z+3*2z*z)
=（14z^2)/(-6z^2)
=-7/3