We have (a + b)2 = a2 + 2ab + b2
So (x + \(\frac{1}{x}\))2 = x2 + 2 x (x) x \(\frac{1}{x}\) + \(\frac{1}{x^2}\)
= x2 + 2 + \(\frac{1}{x^2}\)
= x2 + \(\frac{1}{x^2}\) + 2
= 23 + 2
∵ x2 + \(\frac{1}{x^2}\) = 23
(x + \(\frac{1}{x}\))2 = 25
(x + \(\frac{1}{x}\))2 = 52
x + \(\frac{1}{x}\) = 5