If a,b,c are positive numbers. Prove that ((1+a)(1+b)(1+c))^7 7^7 × a^4 × b^4 × c^4

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If a,b,c are positive numbers. Prove that ((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4

Arun · Answer

Dear student Repeated application of the AM-GM inequality can be used to prove the above strict inequality. The proof is illustrated below: Regards Arun (askIITians forum expert)

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If a,b,c are positive numbers. Prove that ((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4

If a,b,c are positive numbers. Prove that
((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4

1 Answers

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If a,b,c are positive numbers. Prove that ((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4

If a,b,c are positive numbers. Prove that ((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4

1 Answers

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Other Related Questions on Algebra

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If a,b,c are positive numbers. Prove that
((1+a)(1+b)(1+c))^7 > 7^7 × a^4 × b^4 × c^4