( I have tried and failed) Rearrange the following: ((x+a)2 + (x-a)2)/ 2x = 1/x

Answer is= +/- √(1-a2)

Show a clear working out please.

Assuming that you mean [(x+a)^2 + (x-a)^2] / (2x) = 1/x:

Clearing fractions:
(x+a)^2 + (x-a)^2 = (1/x) * 2x
==> (x^2 + 2ax + a^2) + (x^2 - 2ax + a^2) = 2
==> 2x^2 + 2a^2 = 2

Solve for x:
x^2 + a^2 = 1
==> x^2 = 1 - a^2
==> x = ±√(1 - a^2).

I hope this helps!