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CGP EDU Academic Team
Published on: August 14, 2026
If a i >0 for all i = 1,2,3 .........n then prove that
(1 + a 1 + a 21 ) (1 + a 2 + a 22 ) ......... (1 + a n + a 2n ) ≥ 3 n (a 1 a 2 a 3 ...... a n )
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Using A.M. ≥ G.M.
≥ a 1 ⇒ 1 + a 1 + a 21 ≥ 3a 1
similarly 1 + a 2 + a 22 ≥ 3a 2
: : :
1 +a n + a 2n ≥ 3a n
multiplying
(1 + a 1 + a 21 ) (1 + a 2 + a 22 ) .........(1 + a n + a 2n ) ≥ 3 n (a 1 a 2 a 3 ...... a n )
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