If $$x \ne 0,$$   $$y \ne 0$$   and $$z \ne 0$$   and $$\frac{1}{{{x^2}}}$$  + $$\frac{1}{{{y^2}}}$$  + $$\frac{1}{{{z^2}}}$$  = $$\frac{1}{{xy}}$$  + $$\frac{1}{{yz}}$$  + $$\frac{1}{{zx}}$$  then the relation among x, y, z is?

A. x + y + y = 0

B. x + y = z

C. $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$$

D. x = y = z

Answer: Option D

Solution(By Examveda Team)

$$\frac{1}{{{x^2}}} + \frac{1}{{{y^2}}} + \frac{1}{{{z^2}}} = \frac{1}{{xy}} + \frac{1}{{yz}} + \frac{1}{{zx}}$$
Go through option D take x = y = z
$$\eqalign{ & \frac{1}{{{x^2}}} + \frac{1}{{{x^2}}} + \frac{1}{{{x^2}}} = \frac{1}{{x^2}} + \frac{1}{{x^2}} + \frac{1}{{x^2}} \cr & \therefore {\text{Option 'D' is right}} \cr} $$