Question

Arithmetic mean of 2 numbers is 127.5 and geometric mean is 60 find the val

Answer 1

Let the numbers be x and y. Given,
$\frac{x + y}{2} = 127.5 \\ x + y = 255 - - - (1) \\ \sqrt{xy} = 60 \\ xy = 3600 \\ y = \frac{3600}{x} \\ substituting \: \: in \: \: (1) \\ x + \frac{3600}{x} = 255 \\ {x}^{2} - 255x + 3600 = 0 \\ (x - 15)(x - 240) = 0 \\ x = 15 \: \: or \: \: 240 \\ from \: \: (1) \: \: y = 240 \: \: or \: \: 15$
Numbers are 15 & 240