已知2/x=3/y=7/z,求xy+xz+yz/x^2+y^2+z^2
问题描述：
已知2/x=3/y=7/z,求xy+xz+yz/x^2+y^2+z^2
答
令2/x=3/y=7/z=k
∴x=2/k
y=3/k
z=7/k
∴(xy+xz+yz)/(x^2+y^2+z^2)
=(2/k*3/k+2/k*7/k+3/k*7/k)/(4/k²+9/k²+49/k²)
=(6/k²+14/k²+21/k²)/(62/k²)
=(41/k²)/(62/k²)
=41/62