First slide

Geometric progression

Question

If the G.M of two non –zero positive numbers is to their A.M is 12:13 then numbers are in the ratio

Moderate

A

5:8
B

4:9
C

6:11
D

3:8

Solution

$\frac{\sqrt{a b}}{\frac{a + b}{2}} = \frac{12}{13}$
$\begin{array}{l} \frac{\sqrt{a b}}{a + b} = \frac{6}{13} \\ 169 a b = 36 (a + b)^{2} \\ \frac{a^{2} + b^{2} + 2 a b}{a b} = \frac{169}{36} \\ \frac{a}{b} + \frac{b}{a} = \frac{169}{36} - 2 = \frac{97}{36} \\ \Rightarrow a: b = 4 : 9 \end{array}$

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