3x-2y-6z=0

Solution: x=4/3y, z= 1/3y.

So x:y:z=4:3: 1.

x=4z，y=3z

x^2+y^2+z^2/2x^2+y^2-z^2

=( 16+9+ 1)/(32+9- 1)

= 13/20

a+ 1/b = b+ 1/c = c+ 1/a

Multiply abc at the same time and you get

aabc+ac=abcb+ab=abcc+bc

By aabc+ac=abcb+ab

Get ABC (a-b) = a (b-c)...( 1)

By abcb+ab=abcc+bc

Get ABC (b-c) = b (c-a) =-b (a-c)...(2)

By aabc+ac=abcc+bc

Get ABC (a-c) = c (b-a) =-c (a-b)...(3)

( 1)(2)(3)

(abc)^3=abc

a≠b≠c

abc≠0

(abc)^2= 1

a^2b^2c^2= 1