수학동아 - 폴리매스

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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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함께 풀고 싶은 문제

나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.

[문장제 문제&개념응용] ［대수학］슈어 부등식

장OO 2021.02.16 02:22 조회 433

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

다음 부등식을 '슈어 부등식(Schur's Inequality)' 이라고 합니다.

$a^r(a-b)(a-c)+b^r(b-c)(b-a)+c^r(c-a)(c-b)\geq 0$

슈어 부등식은 $a, b, c\in \mathbb{R}^+, r=1$ 일 때 성립함이 알려져 있습니다.

이때, 이 사실을 이용하여 슈어 부등식이 $a, b, c\in \mathbb{R}^+, r=-2$ 일 때에도 성립함을 보이시오.

(슈어 부등식은 $a, b, c\in \mathbb{R}^+, r\in \mathbb{R}$ 일 때 성립한다는 것이 알려져 있고, 이를 증명하고 이용해서 해결하셨다면 부분해결을 드리겠습니다.)

(슈어 부등식이 $a, b, c\in \mathbb{R}^+, r=1$ 일 때 성립함이 알려져 있다는 것을 이용해서 해결하셨다면 해결을 드리겠습니다.)

이전글 '대수'롭지 않은 기하 문제(라고 하긴 그런 대수문제(라고 하긴 좀 그런 기하무..))

다음글 ［경우의 수］［정수론］국교제도 폐지 반대주의

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