First slide

Means - A.M/G.M/H.M

Question

If one geometric $G$ and two arithmetic means $A_{1}$ and $A_{2}$ are inserted between two distinct positive numbers, then $(\frac{2 A_{1} - A_{2}}{G}) (\frac{2 A_{2} - A_{1}}{G})$ equal to

Moderate

A

0
B

1
C

-1.5
D

-2.5

Solution

Let two distinct positive numbers be $a$ and $b .$
We have
$2 A_{1} - A_{2} = 2 (a + d) - (a + 2 d) = a$
and $2 A_{2} - A_{1} = 2 (b - d) - (b - 2 d) = b$
Thus, $(\frac{2 A_{1} - A_{2}}{G}) (\frac{2 A_{2} - A_{1}}{G}) = \frac{a b}{G^{2}} = 1$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App