3/x=5/y=7/z,则xy+yz+zx/x^2-2y^2+3z^2=

3/x=5/y=7/z,则xy+yz+zx/x^2-2y^2+3z^2=
3/x=5/y=7/z,则xy+yz+zx/x^2-2y^2+3z^2=

3/x=5/y=7/z,则xy+yz+zx/x^2-2y^2+3z^2=
答：
设3/x=5/y=7/z=1/k,则有：
x=3k,y=5k,z=7k
代入得：
(xy+yz+zx) / (x^2-2y^2+3z^2)
=(15k^2+35k^2+21k^2) / (9k^2-50k^2+147k^2)
=71/106