Given that (p = xfrac{1}{x} andhspace{1mm}q = x^2 + frac{1}{x^2}) express q in terms of p.

A.
(p^{2} + 2) 
B.
(p – 2) ^{2} 
C.
(p + 2) ^{2} 
D.
(p^{2} – 2)
Correct Answer: Option 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)