Question

the arithematic mean of two numbers is 10 while their geometric mean is 8. calculate the two numbers.

Answer 1

Let the numbers be x and y
$\frac{x + y}{2} = 10 \\ x + y = 20 - - - (1) \\ \sqrt{xy} = 8 \\ xy = 64 \\ substituting \: \: from \: \: (1) \\ x \times (20 - x) = 64 \\ {x}^{2} - 20x + 64 = 0 \\ (x - 4)(x - 16) = 0 \\ x = 4 \: \: or \: \: 16 \\ thus \: \: y = 16 \: \: or \: \: 4$
Therefore, the numbers are 4 and 16