수학동아 - 폴리매스

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Function: _error_handler

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/controllers/ver3/Contents.php
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Function: _error_handler

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

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Function: get_footer

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [대수]평균 사이의 관계

△π 2020.05.05 07:41 조회 781

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

(1) $0\leq a\leq b$ 인 실수 a,b에 대해,

$a\leq \frac{2ab}{a+b}\leq \sqrt{ab}\leq \frac{b-a}{lnb-lna}\leq \frac{a+b}{2}\leq \frac{\sqrt{a^{2}+b^{2}}}{2} \leq \frac{a^{2}+b^{2}}{a+b}\leq b$

임을 보여라.

(2) 반원이 있다. 반원의 지름 AB 위에 한 점 C가 있다. AC=a, BC=b일 때, 산술평균, 기하평균, 조화평균, 제곱근 멱 평균을 그 반 원위에 나타내고, 이를 이용해 위의 성분중 로그평균과 반조화평균을 뺀 나머지를 증명하여라.

(3)A,B,C에 대해, (A+B)/2=C일 때, 이를 '산술평균쌍'이라 하자. 이들 관계중 산술평균쌍, 기하평균쌍, 제곱근 멱 평균쌍을 찾아라.

(4)a,b 둘 중 하나만 음수라면 이 식은 자명하게 성립하지 않는다.(루트 안이 마이너스). 그러면 a,b 둘 다 음수라면 이 식은 성립하지 않을까? 하지만 아니다. 그 이유를 구하여라.

이전글 [수의 조합] 수의 조합

다음글 [기하]정삼각형과 원(재재업)

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supermathe Lv.6 2020.05.08 19:59

ㅎㄷㄷ 산기 증명만해도...........,

,

,

,

,

,

,

,,

,

,

,

,

,

,

,

,

,

이정도 나올듯

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