WBJEE · Maths · Sequences and Series
If three positive real numbers \(a, b, c\) are in A.P. and \(a b c=4\) then minimum possible value of \(b\) is
- A \(2^{3 / 2}\)
- B \(2^{2 / 3}\)
- C \(2^{1 / 3}\)
- D \(2^{5 / 2}\)
Answer & Solution
Correct Answer
(B) \(2^{2 / 3}\)
Step-by-step Solution
Detailed explanation
\[ \text { Hints } \begin{aligned} & (b-d) b(b+d)=4 \\ & \left(b^2-d^2\right) b=4 \\ & b^3=4+d^2 b \\ & b^3 \geq 4 \Rightarrow b \geq(2)^{2 / 3} \end{aligned} \]
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