Question

AM & GM between a & b is 10 & 8. Find a & b

Answer 1

Step-by-step explanation:

Given:

AM = 10

$\implies \: \frac{a + b}{2} = 10 \\ \implies \: a + b = 20.....(1) \\ GM = 8 \\ \implies\sqrt{ab} = 8 \\ \implies \: ab = 64...(2) \\ \because \: (a - b)^{2} = (a + b) ^{2} - 4ab \\ \therefore \: (a - b)^{2} = (20) ^{2} - 4 \times 64 \\ \therefore \: (a - b)^{2}= 400 - 256 \\ \therefore \: (a - b)^{2}= 144 \\ \therefore a - b = 12.....(3) \\ on \: solving \: equations \: (1) \: and \: (3) \: we \: find : \\ a = 16 \\ b = 4$