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Inequalities!

Can you prove this? \[(a^5 - a^2 + 3)(b^5 - b^2 + 3)(c^5 - c^2 + 3) \ge (a+b+c)^3 .\]

Note by Gokul Kumar
2 years, 4 months ago

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We can solve it using Holder's inequality..this problem appeared in USAMO 2004

Ayush Garg - 2 years, 4 months ago

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can you write the solution to this problem?

Gokul Kumar - 2 years, 4 months ago

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http://www.artofproblemsolving.com/wiki/index.php/2004USAMOProblems/Problem_5

Edit: if the link doesn't work, just search "USAMO 2004 problem 5" on Google and you'll find an AoPS link with full solutions.

Mathh Mathh - 2 years, 3 months ago

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First use rearrangement inequality and then Holder

Kushal Padole - 1 year, 11 months ago

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You can find some full solutions on AoPS after searching "USAMO 2004 Problem 5" on Google.

Mathh Mathh - 1 year, 11 months ago

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Ya I saw that long back. I just felt like thanks for writing his suggestion.

Gokul Kumar - 1 year, 11 months ago

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Yeah thanks

Gokul Kumar - 1 year, 11 months ago

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