Let a 1 , a 2 , a 3 be any positive real numbers, then which of the following statement…

Mathematics · JEE Main · NTA Exams — Progression and Series

1. \(3 a_{1} a_{2} a_{3} \leq a_{1}^{3}+a_{2}^{3}+a_{3}^{3}\)
2. \(\frac{a_{1}}{a_{2}}+\frac{a_{2}}{a_{3}}+\frac{a_{3}}{a_{1}} \geq 3\)
3. \(\left(a_{1}+a_{2}+a_{3}\right)\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}\right) \geq 9\)
4. \(\left(a_{1}+a_{2}+a_{3}\right)\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}\right)^{3} \leq 27\)

Answer

(D) (a_ 1 +a_ 2 +a_ 3 ) ( 1 a_ 1 + 1 a_ 2 + 1 a_ 3 )^ 3 27

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