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?

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