If f(x + 1/x) = )x^2 + 1/x^2) for all x ϵ R – {0} then write an expression for f(x). ​

Question

If f\((x + \frac{1}x)\) = \((x^2 + \frac{1}{x^2})\) for all x ϵ R – {0} then write an expression for f(x).

Answer 1

f\((x + \frac{1}x)\) = \((x^2 + \frac{1}{x^2})\)

 Let y = x + 1/x

xy = x² + 1

x² - xy + 1 = 0