수학동아 - 폴리매스

함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [대수] 삼차방정식의 실근의 성질

베네딕트0724 2020.08.24 00:53 조회 540

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

$x^3-3x+1=0$ 의 실근 a,b,c(a를 구하여라.

책에서 풀이 보고 멘탈이 나가서 올립니다 ㅋㅋㅋ 이거 3배각 안 쓰고 풀 수 있을까요?

(수정) 문제 수식이 자꾸 짤리네요. 조건과 구하려는 값은 대댓글로 남겼습니다!

이전글 [정수] 시그마 나누기

다음글 이게 유리수라고?

이 문제 어떠셨나요?

글쎄요

어려워요

문제 찜하기 목록보기

댓글 작성하기

리프 Lv.7 2020.08.24 00:56

~~카르다노의 해법~~

댓글 작성하기 좋아요0 댓글수1
- 베네딕트0724 Lv.6 2020.08.24 00:58
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: mkdir(): Permission denied
  
  Filename: libraries/Common.php
  
  Line Number: 202
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 202
  Function: mkdir
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: file_put_contents(/DATA/upload/polymath/latex/6466159f72b305b54f2ed379edf6579d.gif): failed to open stream: No such file or directory
  
  Filename: libraries/Common.php
  
  Line Number: 213
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 213
  Function: file_put_contents
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  아 이거 문제가 이상하게 짤렸네요
  
  a<b<c일 때, $a^2+b^2-a-c$ 를 구하는 문제입니다. 카르다노로 해 구한다 해도 힘들죠 ㅋㅋㅋ
  
  좋아요0
여백 패르마 Lv.5 2020.08.24 02:31

아 KMO 고등 기출이다!!

.....못 풀겠네요

댓글 작성하기 좋아요0 댓글수2
- 베네딕트0724 Lv.6 2020.08.24 05:24
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: mkdir(): Permission denied
  
  Filename: libraries/Common.php
  
  Line Number: 202
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 202
  Function: mkdir
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: file_put_contents(/DATA/upload/polymath/latex/57f3c524a61b830b671d312d62393ebf.gif): failed to open stream: No such file or directory
  
  Filename: libraries/Common.php
  
  Line Number: 213
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 213
  Function: file_put_contents
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: mkdir(): Permission denied
  
  Filename: libraries/Common.php
  
  Line Number: 202
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 202
  Function: mkdir
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: file_put_contents(/DATA/upload/polymath/latex/d252c39b3b889a64de1c5ef44950c72b.gif): failed to open stream: No such file or directory
  
  Filename: libraries/Common.php
  
  Line Number: 213
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 213
  Function: file_put_contents
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: mkdir(): Permission denied
  
  Filename: libraries/Common.php
  
  Line Number: 202
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 202
  Function: mkdir
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  A PHP Error was encountered
  
  Severity: Warning
  
  Message: file_put_contents(/DATA/upload/polymath/latex/8e1683f1d16fe9350aaef2d7b0613b58.gif): failed to open stream: No such file or directory
  
  Filename: libraries/Common.php
  
  Line Number: 213
  
  Backtrace:
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 213
  Function: file_put_contents
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
  Line: 236
  Function: getLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
  Line: 200
  Function: parseLatexImg
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
  Line: 343
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
  Line: 558
  Function: view
  
  File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
  Line: 315
  Function: require_once
  
  2010년 기출 맞습니다! 찾아보니까 3배각 안 쓰는 풀이도 있네요. 이걸 어떻게 생각해내지 싶긴 한데요 ㅋㅋㅋ
  
  $(t^2-2)^3-3(t^2-2)+1=(t^2-3t+1)(t^2-3t-1)$ 이렇게 시작해서 정리하면 나와요.
  
  3배각 쓰는 풀이는
  
  $cos3\theta =4cos^3\theta -3cos\theta$ 에서 $\theta =20^{\circ}$ 대입하고 시작합니다.
  
  둘 다 생각해내기 어려운 해법이죠 ㅠㅠ
  
  되게 오랫동안 매달렸는데 못 풀었어요 ㅋㅋ
  
  좋아요0
- 리프 Lv.7 2020.08.26 03:41
  
  삼배각 쓰는 해법은 각 삼등분 불가능 증명을 알고 있으면 쉽게 떠올릴 수도 있을 것 같네요. 그 증명에서도 cos 20 계산해서 문제의 식 보고 알아챌 수도 있을 것 같다는 생각이 드네요 ㅇㅅㅇ
  
  좋아요0
sicma Lv.11 2021.01.26 07:38

삼배각 안 쓰고 풀 수 있을 것 같은데...

댓글 작성하기 좋아요0 댓글수0