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if a,b,c>0 prove that[(1+a)(1+b)(1+c)]^7>7^7a^4b^4c^4

if a,b,c>0 prove that[(1+a)(1+b)(1+c)]^7>7^7a^4b^4c^4

Grade:12th pass

2 Answers

mycroft holmes
272 Points
5 years ago
Repeated application of the AM-GM inequality can be used to prove the above strict inequality. The proof is illustrated below:
 
mycroft holmes
272 Points
5 years ago
I had to edit the proof above for using the wrong symbol
 
Repeated application of the AM-GM inequality can be used to prove the above strict inequality. The proof is illustrated below:
 

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