2022 · Q30
The arithmetic mean and the geometric mean of two positive numbers p and q (p > q) are A and G respectively. Which one of the following is correct?
Elementary MathematicsAlgebra
- AA > G
- BG > A
- CA = G
- DA² = G
Explanation
For distinct positive numbers the AM-GM inequality is strict: A > G. (Equality holds only when p = q.) Hence the keyed option is A.