In English, please?nafistiham wrote:ভাঈয়া, একপাশে $a,b,c$ আর অন্য পাশে $c,a,b$ গুন করেছিsourav das wrote:@ willpower : It's because of re-arrangement inequality.
@nafistihamHow?nafistiham wrote:again,
\[\Rightarrow a^{4}+b^{4}+c^{4} \geq a^{2}bc+b^{2}ca+c^{2}ab\]
rearrangement inequality দিয়ে কি এটা বলা যায় না?
Algebra: Inequalities
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein
Re: Algebra: Inequalities
এভাবে সর্বসম্মুখে কোন কপিরাইটেড জিনিসের ডাউনলোড লিঙ্ক পোস্ট করিস না।nafistiham wrote:ifile.it/zlct48/ebooksclub.org__Inequalities__A_Mathematical_Olympiad_Approach.pdf
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- nafistiham
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Re: Algebra: Inequalities
মাহী পোস্ট করছিলো । আমী কপি করে দেখি হয় না। তাই এভাবে করলাম ।
*Mahi* wrote:Inequalities : A Mathematical Olympiad ApproachiPavel wrote:"ক্যাম্পের পাঠ্যপুস্তক সবাইকে নিজ দায়িত্ব সংগ্রহ করতে হবে"
পাঠ্যপুস্তক কি কি?ডাউনলোড লিংটা একটু দেন
মাহি
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: Algebra: Inequalities
I understood rearrangement inequality. However, I'm not familiar with this notation/method (quote below). Could anyone kindly explain?
Nadim Ul Abrar wrote:a) rearrangement .
b)
$a^{4}+b^{4}+c^{4}=3[4,0,0]$
$abc(a+b+c)=3[2,1,1]$
$[4,0,0] \geq 3[2,1,1]$
so proved
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein
Re: Algebra: Inequalities
This is called "Muirhead theorem", and the $[a,b,...,x]$ notation is for n-tuples. You can know it from any book of inequality or google.
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Nur Muhammad Shafiullah | Mahi
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