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