A Crazy Inequality under a Bizarre Condition | Turkish Junior Mathematical Olympiad 2012 Problem 3

[@xxxprawn8374]

that’s actually pretty interesting for a jmo problem

[@mukaddastaj5223]

Yessss, Hölder was used so accurately, loved the video immediately!) Thank u, i enjoy ur channel, the contents are so helpful))

[@andreben6224]

WOW such technique! It's amazing, I don't know if I could have found such a solution, so I really enjoyed the video.

[@srikanthtupurani6316]

a(a^2+b^3+c^3) + two similar terms. This thing we should multiply with the expression.This is the most natural thing that anyone will go for. I don't understand how they set these problem. It appears more like reverse engineering. Most interesting thing is knowing how olympiad problems are created. I feel if we know how these problems are created we may be able to solve some annoying olympiad problems.

[@ravirajamadan]

Brillant way to solve the inequality. learnt a new inequality today!.

[@xriccardo1831]

I love your channel, keep it up

[@letsthinkcritically]

Thank you very much!

[@cycklist]

This was really interesting, thank you. Also thanks for saying zed and not 'zee'. 👍

[@johnnath4137]

'zee' goes with math and 'zed' with maths (he does say 'maths').

[@kuab1313]

@@johnnath4137 No, it's just "zed" going with English.

[@Deathranger999]

@@kuab1313 No, just “zed” going with non-American dialects of English. Just because you don’t like it doesn’t mean it doesn’t count lmfao.

[@kuab1313]

@@Deathranger999 It's not about me liking it or not, it's about making errors in English or not.

[@Deathranger999]

@@kuab1313 Lol. You think that different dialects are incorrect. That’s so cute.

[@johnnath4137]

What is a typical age for junior IMO contestants? This seems a bit heavy for juniors.

[@mukaddastaj5223]

It doesn't, actually) I really struggle with other problems, so this one isn't that hard :) But hose number theory ones😥

[@arunsahoo5603]

This is Regionals level olmpiads question right

[@Bossudeboss898]

Great video! Keep it up! 👍

[@srikanthtupurani6316]

Cauchy schwartz appears to be helpful in solving this problem.

[@whiteboardmath9454]

My first thought was that the condition that a^3+ b^3+ c^3= a^4+ b^4+ c^4 must imply that one possible solution is easily 1, and since 1^n, for n is a positive integer is always 1, I got a+b+c=3, and then 3/3=1, and we have proven that 1 is one possible real solution.

[@huseyinyigitemekci-fm8vf]

Nice solution. That should be round 2 or TST I think

[@giuseppebassi7406]

Thank you for this video, very helpful

[@gabrielius4603]

Hello can you explain how you got that on 5:55?

[@omegawarrior3080]

If you take the original inequality and multiply by a(a^2+b^3+c^3)+b(b^2+a^3+c^3)+c(c^2+a^3+b^3) you get by cauchy that it is greater or equal to (a+b+c) ^2. Then you can divide by the same thing. LHS is the original expression and the denominator is another way to write a(a^2+b^3+c^3)+b(b^2+a^3+c^3)+c(c^2+a^3+b^3)

[@gabrielius4603]

@@omegawarrior3080 Thanks a lot

[@agastyaagrawal4688]

Hi. would you recommend some books for algebra?

[@letsthinkcritically]

I have received many similar requests. I am going to start introducing my favourite Mathematics books through Community Posts very soon 👍🏻

[@dhrubalaskar9587]

did u win gold medal in the imo 😐😐

[@nodiradullayeva7755]

Well done

[@ГригорийЕ-в5ь]

Good problem, but the author overcomplicated a simple problem that can be solved with closed eyes.

[@juliancarax4797]

how is a^3+b^3+c^^3 the same as a^4+b^4+c^4

[@sampasaha2649]

It is written in the question.

[@juliancarax4797]

@@sampasaha2649 oh wow so helpful

[@parthivreddy7989]

Thank you

[@9810johnny]

3:35 love it ! XD 1 1 1 -> LHS

[@beautykumari3883]

OverPowered Inequality Problem

[@ДмитрийСкрипник-с7щ]

Лемма Титу.

[@mateuspacheco780]

ok

[@Лайла.Р]

W O W

[@crazy4hitman755]

😍

[@aiseop31415]

You are from japan , right?

[@letsthinkcritically]

Akash Raj No, I am from Hong Kong.

[@johnnath4137]

@@letsthinkcritically Are you related to Terence Tau? Maybe you are his uncle?

[@luoluoye9620]

@@johnnath4137 LoL.....

[@gmncnr]

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