Let A1, A2, be two AM's and G1, G2, be two GM's between a and b, then (A1 + A2) / G1G2 is equal to _____Options(a+b) / 2ab(a+b) / abNone of these2ab / (a+b)
Question
Let A1, A2, be two AM's and G1, G2, be two GM's between a and b, then is equal to _____
Options
(a+b) / 2ab
(a+b) / ab
None of these
2ab / (a+b)
Solution
The correct answer is (a+b) / 2ab.
Here's the step by step solution:
Given that A1 and A2 are two arithmetic means between a and b, we have:
A1 = (a + b) / 2 and A2 = (a + b) / 2
So, A1 + A2 = a + b
Given that G1 and G2 are two geometric means between a and b, we have:
G1 = sqrt(ab) and G2 = sqrt(ab)
So, G1 * G2 = ab
Therefore, (A1 + A2) / G1G2 = (a + b) / ab
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