If one arithmetic mean (AM) \(a\) and two geometric means (GM) \(p\) and \(q\) are inserted between two positive numbers, the value of \(p^3 + q^3\) is:
Let two numbers be \( 1 \) and \( 8 \). \[\] Arithmetic Mean (AM) \( a \) of \( 1 \) and \( 8 \): \[ AM = \frac{9}{2} \] Geometric Means (GM) \( p \) and \( q \): \[ GM = 2, 4 \] Sum of cubes of \( p \) and \( q \): \[ p^3 + q^3 = 8 + 64 = 72 \] Relation between sum of cubes and product: \[ p^3 + q^3 = 2a.pq \]
Reinforce your conceptual grasp with related questions from NIMCET 2024:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →