Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityEasy2 minPYQ_2017

MathematicsEasystatement

If three positive numbers $a$ , $b$ and $c$ are in A.P. such that $a b c = 8$ , then the minimum possible value of $b$ is:

Answer:

Solution:

As $a + c = 2 b$ ,

Using $A . M \geq G . M$

$\Rightarrow \frac{a + b + c}{3} \geq {(a b c)}^{\frac{1}{3}}$

$\Rightarrow \frac{3 b}{3} \geq {(8)}^{\frac{1}{3}}$

$b \geq 2$

$∴ b_{m i n} = 2$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: PYQ_2017

Loading discussions...