Question

The arithmetic mean of two numbers is 10 and their geometric mean is 8

Answer 1

$let \: the \: number \: be \: x \: and \: y \\ \:arithmetic \: mean \\ \\ = \frac{x + y}{2} = 10 \\ x + y = 20 \\ geometric \: mean \\ = \sqrt{xy} = 8 \\ xy = 64$
$x = \frac{64}{y} \\ x + y = 20 \\ \frac{64}{y } + y = 20 \\ {y }^{2} - 20y + 64 \\ y = 4 \: or \: 16 \\ x = 16 \: or \: 4$