수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 삼차방정식

cjmoon 2020.02.07 21:31 조회 577

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

삼차방정식 근의 공식은

삼차방정식 $ax^{3}+bx^{2}+cx+d$ =0에서의 근을 $x_{1}$ , $x_{2}$ , $x_{3}$ 라 할 때,

$x_{1}=-\frac{b}{3a}$

$-\frac{1}{3a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b+\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

$-\frac{1}{3a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b-\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

$x_{2}=-\frac{b}{3a}$

$+\frac{1+i\sqrt{3}}{6a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b+\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

$+\frac{1-i\sqrt{3}}{6a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b-\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

$x_{3}=-\frac{b}{3a}$

$+\frac{1-i\sqrt{3}}{6a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b+\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

$+\frac{1+i\sqrt{3}}{6a}\sqrt[3]{\frac{2b^{3}-9abc+27a^{2}b-\sqrt{(2b^{3}-9abc+27a^{2}b)^{2}-4(b^{2}-3ac)^{3}}}{2}}$

이다.

왜 그럴까?

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도전

Abiria♡ Lv.8 2020.02.09 06:41 비밀댓글

확인요청중

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- cjmoon Lv.6 2020.02.10 00:12 비밀댓글
  
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