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Question: Answered & Verified by Expert
If three positive real numbers $a, b, c$ are in A.P. and $a b c=4$ then minimum possible value of $b$ is
MathematicsSequences and SeriesWBJEEWBJEE 2009
Options:
  • A $2^{3 / 2}$
  • B $2^{2 / 3}$
  • C $2^{1 / 3}$
  • D $2^{5 / 2}$
Solution:
2603 Upvotes Verified Answer
The correct answer is: $2^{2 / 3}$
$$
\text { Hints } \begin{aligned}
& (b-d) b(b+d)=4 \\
& \left(b^2-d^2\right) b=4 \\
& b^3=4+d^2 b \\
& b^3 \geq 4 \Rightarrow b \geq(2)^{2 / 3}
\end{aligned}
$$

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