+3 votes
in JEE by kratos

If A1, A2 are two AMs between two numbers a and b, then express (2A1-A2)(2A2-A1) in terms of a and b.

1 Answer

+6 votes
by kratos
 
Best answer

Given :

A1 and A2 are two AM between a and b.

Let d be the common difference of this A.P. Clearly, it contains (n+2) terms = 2+2 = 4 terms
=> b = (n+2)th term = 4th term

Now, Putting the value of n = 2 in A1 and A2 we get,

A1 = (2a+b) / 3 -------------(1)

A2 = (a+2b) / 3 -------------(2)

Fro question :

=> (2A1 – A2)(2A2-A1) = [2(2a+b)/3-(a+2b)/3] [2/3(a+2b)-(2a+b)/3]

*=> (2A1 – A2)(2A2-A1) = ab**

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