​ If x - 1/x = - 1, find the value of x^2 + 1/x^2

Question

If x - \(\frac{1}{x}\) = -1, find the value of x² + \(\frac{1}{x^2}\)

Answer 1

Here, we will use (a - b)² = a² + b² - 2ab

(x - \(\frac{1}{x}\)) = (-1)

(x - \(\frac{1}{x}\))² = (-1)²

(x)² + (\(\frac{1}{x}\))² - 2 x x x \(\frac{1}{x}\) = 1

x² + \(\frac{1}{x^2}\) = 1 + 2

x² + \(\frac{1}{x^2}\) = 3