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Question

From given A.P i.e., a b2 c3, a2 b3 c4, a3 b4 c5, get the value of abc __

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Solution

Observe that a + b + c is a part of AM of a, b, c i.e., (a+b+c)3 as AM GM & HM,

We can get minimum value of AM from this relation : AM GM

Using AM GM a + b + c 3 (abc)13 ------------(1)

We need value of abc

Given a b2 c3, a2 b3 c4, a3 b4 c5 are in A.P.

2a2b3c4ab2c3 = ab2c3ab2c3 + a3b4c5ab2c3

2abc = 1 + a2 b2 c2

(abc)2 - 2abc + 1 = 0

(abc1)2 = 0

So, abc = 1


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