List of top Mathematics Questions on relationship between a.m. and g.m. asked in COMEDK UGET

If the arithmetic mean between two positive numbers is \(10\) and the geometric mean is \(8\), then the numbers are:

Let \( A \) and \( G \) denote the arithmetic mean and geometric mean of positive real numbers \( 5^x \) and \( 5^{1 - x} \). Then the minimum value of the expression \[ 5^x + 5^{1 - x}, \text{ where } x \in \mathbb{R}, \text{ is:} \]