2024 · Q21
If p = √((a+√(a²+b³))) + √((a-√(a²+b³))), then what is p³ + 3bp equal to ?
Elementary MathematicsAlgebra
- A-2a
- Ba
- C2a
- D3a
Explanation
Cubing p = ∛A + ∛B gives p³ = A + B + 3∛(AB)·p, with A + B = 2a and AB = a² − (a² + b³) = −b³. Hence p³ = 2a − 3bp. Rearranging gives p³ + 3bp = 2a, option (c).