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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, 1 month ago

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We can solve it using Holder's inequality..this problem appeared in USAMO 2004 Ayush Garg · 2 years, 1 month ago

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@Ayush Garg can you write the solution to this problem? Gokul Kumar · 2 years, 1 month ago

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@Gokul Kumar 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 ago

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First use rearrangement inequality and then Holder Kushal Padole · 1 year, 8 months ago

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@Kushal Padole You can find some full solutions on AoPS after searching "USAMO 2004 Problem 5" on Google. Mathh Mathh · 1 year, 8 months ago

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@Mathh Mathh Ya I saw that long back. I just felt like thanks for writing his suggestion. Gokul Kumar · 1 year, 8 months ago

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@Kushal Padole Yeah thanks Gokul Kumar · 1 year, 8 months ago

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