Question

A.M and G.M of two positive integers a and be (a<b) are respectively 5 and 4; find a and b.​

Answer 1

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \\ values \: of \: a \: and \: b \\ \\ so \: here \\ \: for \: certain \: two \: numbers \\ their \: respective \: </p><p>A.M \: and \: G.M \: are \\ A.M = 5 \\ G.M = 4 \\ \\ thus \: then \\ \sqrt{ab} = 4 \\ ab = 16 \\ thus \: then \\ \: \\ a = \frac{16}{b} \: \: \: \: \: \: \: (1) \\ \\ \frac{a + b}{2} = 5 \\ \\ a + b = 10$

$\frac{16}{b} + b = 10 \\ \\ b {}^{2} + 16 = 10b \\ \\ b {}^{2} - 10b + 16 = 0 \\ \\ b {}^{2} - 8b - 2b + 16 = 0 \\ \\ (b - 8)(b - 2) = 0 \\ \\ b - 8 = 0 \: \: or \: \: b - 2 = 0 \\ \\ b = 8 \: \: or \: \: b = 2\\ \\ if \: b = 8 \\ \\ a = \frac{16}{8} \\ \\ a = 2 \\ \\ if \: b = 2 \\ \\ a = \frac{16}{2} \\ \\ a = 8$

$thus \: the n \\ \: required \: two \: numbers \: are \\ 8 \: and \: 2$