If a , b , c are positive real numbers, then b a + c b + a c is greater than or equal to

A.M. ≥ G.M. for b a , c b , a c : 3 b a + c b + a c ≥ ( b a ⋅ c b ⋅ a c ) 1/3 = 1 . So the sum is at least 3.

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

If $a, b, c$ are positive real numbers, then $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is greater than or equal to

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Solution:

A.M. $\geq$ G.M. for $\frac{a}{b}, \frac{b}{c}, \frac{c}{a} : \frac{\frac{a}{b} + \frac{b}{c} + \frac{c}{a}}{3} \geq (\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{a})^{1/3} = 1$ . So the sum is at least 3.

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

⏱ 2mℹ️ Source: QB

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