If $x + \frac{1}{x} = 5$, what is the value of $x^4 + \frac{1}{x^4}$?

Explanation

Given that– $x + \frac{1}{x} = 5$ Squaring on both sides– $x^2 + \frac{1}{x^2} + 2 = 25$ $x^2 + \frac{1}{x^2} = 23$ again, squaring on both sides– $x^4 + \frac{1}{x^4} + 2 = 529$ $x^4 + \frac{1}{x^4} = 527$