If x^2 + (1/x^2) = 23 find x + (1/x).

Question

If x² + \(\frac{1}{x^2}\) = 23 find x + \(\frac{1}{x}\).

Answer 1

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