Question

Write the two numbers whose arithmetic mean is 25 and geometric mean is 20

Answer 1

(a+b)/2 = 25, or

a+b = 50 …(1). or

b = 50-a



The geometric mean of two numbers, a and b = 20 or

(ab)^0.5 = 20, or

ab = 400 …(2), or


a(40-a) = 400

a^2 - 50a + 400 = 0

(a-10)(a-40) = 0

a = 10 , 40

then b = 40 , 10

Answer 2

let the two nos be x and y
$\frac{x + y}{2} = 25 = > x + y = 50\\ \sqrt{xy} = 20 = > xy = 400 \\ the \: equation \: with \: x \: and \: y \: as \: roots \: is \\ {t}^{2} - 50t + 400 = 0 \\ {t}^{2} - 40t - 10t + 400 = 0 \\ t(t - 40) - 10(t - 40) = 0 \\ (t - 40)(t - 10) = 0 \\ t = 40 \: \: \: or \: \: \: t = 10 \\ then \: the \: two \: nos \: are \: 40 \: and \: 10$