Discussion

If \(x^2 + \dfrac{1}{x^2} = 34\) and \(x\) is positive, then \(x + \dfrac{1}{x}\) equals:

Answer: B

Squaring gives \(\left(x + \dfrac{1}{x}\right)^2 = x^2 + 2 + \dfrac{1}{x^2} = 34 + 2 = 36\), so \(x + \dfrac{1}{x} = 6\) for positive \(x\). The cross term is exactly 2 because \(x\) and \(\dfrac{1}{x}\) multiply to 1, which is what makes this identity so useful.