If x + 1/x = 2, then what is value of x - 1/x ?

Given that, x + 1/x = 2 ...................(i)
On squaring both sides, we get
(x + 1/x)² = 4
⇒ x² + 1/x² + 2 = 4
⇒ x² + 1/x² = 2 ..................................(ii)
Now, we have
(x - 1/x)² = (x² + 1/x²) - 2x X 1/x
now put the value of x² + 1/x²
(x - 1/x)² = 2 - 2 = 0 [from Eq. (ii)]
∴ x - 1/x = 0