2022 · Q37
If p is the difference between a number and its reciprocal and q is the difference between the square of the same number and the square of its reciprocal, then what is p⁴ + 4p² equal to?
Elementary MathematicsAlgebra
- A4q
- B8q
- C4q²
- Dq²
Explanation
q = x²−1/x² = (x−1/x)(x+1/x) = p(x+1/x). Since x²+1/x² = p²+2, squaring gives q² = (p²+2)² − 4 = p⁴+4p². The keyed option is D.