令x/3=y/1=z/2=k
x=3k,y=k,z=2k
(2x^2-2y^2+5z^2)/(xy+yz+zx)
=[2(3k)^2-2k^2+5(2k)^2]/(3k*k+k*2k+3k*2k)
=[2*9k^2-2k^2+5*4k^2]/(3k^2+2k^2+6k^2)
=[18k^2-2k^2+20k^2]/(3k^2+2k^2+6k^2)
=(36k^2)/(11k^2)
=36/11