[JEE Advanced 2002] if a 1 a 2 a n are positive reals with product a fixed
If $a_1,a_2,\dots,a_n$ are positive reals with product a fixed $c$, then the minimum value of $a_1+a_2+\cdots+a_{n-1}+2a_n$ is
(a) $n(2c)^{1/n}$
(b) $(n+1)c^{1/n}$
(c) $2n\,c^{1/n}$
(d) $(n+1)(2c)^{1/n}$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 4d ago
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Correct answer: (a) $n(2c)^{1/n}$
By AM–GM on the $n$ terms $a_1,\dots,a_{n-1},2a_n$ (product $2c$), the sum $\ge n(2c)^{1/n}$.
JEE Advanced 2002 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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