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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] [기하,정수,조합,(대수?)]맞는 문제와 틀린 문제
sicma
2020.11.02 01:21
조회 413
가)x2+bx+6b=0의 해가 모두 정수일때 가능한 실수 b는 총 10개이다.
나)△ABC의 내심을 I, 내접원과 BC,CA의 접점을 각각 D,E라 하고, 직선 AI와 DE의 교점을 P라 하자 BC,AB의 중점을 각각 M,N이라 할때 M,N,P가 일직선에 놓인다.
다)범위가 정해져 있는 2차 함수를 잘 조합하면 3차함수를 만들 수 있다.
라) 집합 {1,2,...,N}의 공집합이 아닌 모든 부분집합을 생각해보자.
이때 각 부분집합레서 원소들의 역수의 곱을 구해, 이것을 모두 합하면 N이 된다.
이 4문재 중에서 맞은 것과 틀린 것을 고르고 그에 대한 풀이를 모두 제시해 주세요.
지금 바로
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