Given that \(p = x-\frac{1}{x} and\hspace{1mm}q = x^2 + \frac{1}{x^2}\) express q in terms of p.
-
(p2 + 2)
- (p - 2) 2
- (p + 2) 2
- (p2 - 2)
The correct answer is: A
Explanation
Given \(p = x - \frac{1}{x}\); \(q = x^2 + \frac{1}{x^2}\).
\(p^2 = (x - \frac{1}{x})(x - \frac{1}{x})\)
\(p^2 = x^2 + \frac{1}{x^2} - 2\)
\(p^2 = q - 2 \implies q = p^2 + 2\)