Question

The arithmetic mean of two numbers is 10; their geometric mean is 8.Find the harmonic mean of the two numbers as well as the two numbers themselves.

Answer 1

Answer:

$a = 16 \\ a = 4 \\ \\ \\ b = 4 \\ b = 16$

$numbers \: are \: 4 \: and \: 16$

Step-by-step explanation:

$\frac{a + b}{2} = 10 \\ \\ a + b = 20 \\ \\ \sqrt{ab} = 8 \\ \\ ab = 64 \\ \\ a + \frac{64}{a} = 20 \\ \\ {a}^{2} - 20a + 64 = 0 \\ (a - 16)(a - 4) = 0 \\ a = 16 \\ a = 4 \\ \\ \\ b = 4 \\ b = 16 \\ \\ numbers \: are \: 4 \: and \: 16$