루트를 이용한 간접조건

사는 이야기/수학사전

루트를 이용한 간접조건

후암동남산 2015. 1. 26. 11:19

1. 분수꼴의 루트

$%EC%9D%BC%EB%B0%98%EC%A0%81%EC%9C%BC%EB%A1%9C%5Cquad%20%5Cfrac%20%7B%20%5Csqrt%20%7B%20b%20%7D%20%7D%7B%20%5Csqrt%20%7B%20a%20%7D%20%7D%3D%5Csqrt%20%7B%20%5Cfrac%20%7B%20b%20%7D%7B%20a%20%7D%20%7D%EA%B0%80%5Cquad%20%EC%84%B1%EB%A6%BD%ED%95%98%EC%A7%80%EB%A7%8C%5C%5C%20b%3E0%2C%5Cquad%20a%3C0%EC%9D%B4%EB%A9%B4%5Cquad%20%5Cfrac%20%7B%20%5Csqrt%20%7B%20b%20%7D%20%7D%7B%20%5Csqrt%20%7B%20a%20%7D%20%7D%3D-%5Csqrt%20%7B%20%5Cfrac%20%7B%20b%20%7D%7B%20a%20%7D%20%7D%EA%B0%80%5Cquad%20%EB%90%9C%EB%8B%A4.%20$

$%EC%99%9C%EB%83%90%ED%95%98%EB%A9%B4%2C%5Cquad%20%EB%B6%84%EB%AA%A8%EA%B0%80%5Cquad%20%EC%9D%8C%EC%88%98%EB%9D%BC%EB%A9%B4%5Cquad%20%EB%B6%84%EB%AA%A8%EC%9D%98%5Cquad%20i%EB%A5%BC%5Cquad%20%EC%8B%A4%EC%88%98%ED%99%94%ED%95%98%EB%A9%B4%5Cquad%20%EA%B2%B0%EA%B5%AD%5Cquad%20%5Ccombi%20%5E%7B%202%20%7D%7B%20i%20%7D%3D-1%EC%9D%B4%EB%AF%80%EB%A1%9C%5Cquad%20%EC%A0%84%EC%B2%B4%EC%97%90%5Cquad%20-%EA%B0%80%5Cquad%20%EB%8D%94%ED%95%B4%EC%A7%80%EA%B8%B0%5Cquad%20%EB%95%8C%EB%AC%B8%EC%9D%B4%EB%8B%A4.%5C%5C%20%EC%98%88%EB%A5%BC%5Cquad%20%EB%93%A4%EC%96%B4%2C%5Cquad%20%5Cfrac%20%7B%20%5Csqrt%20%7B%203%20%7D%20%7D%7B%20%5Csqrt%20%7B%20-2%20%7D%20%7D%3D%5Cfrac%20%7B%20%5Csqrt%20%7B%203%20%7D%20%7D%7B%20%5Csqrt%20%7B%202%20%7Di%20%7D%EC%9D%B4%EB%AF%80%EB%A1%9C%5Cquad%20%EC%8B%A4%EC%88%98%ED%99%94%5Cquad%20%ED%95%98%EA%B8%B0%EC%9C%84%ED%95%B4%5Cquad%20%EB%B6%84%EC%9E%90%EB%B6%84%EB%AA%A8%EC%97%90%5Cquad%20i%EB%A5%BC%5Cquad%20%EA%B3%B1%ED%95%98%EB%A9%B4%5C%5C%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cquad%20%5Cquad%20%3D%5Cfrac%20%7B%20%5Csqrt%20%7B%203%20%7Di%20%7D%7B%20%5Csqrt%20%7B%202%20%7D%5Ccombi%20%5E%7B%202%20%7D%7B%20i%20%7D%20%7D%EC%9D%B8%EB%8D%B0%5Cquad%20i%3D%5Csqrt%20%7B%20-1%20%7D%EC%9D%B4%EA%B3%A0%5Cquad%20%5Ccombi%20%5E%7B%202%20%7D%7B%20i%20%7D%3D-1%EC%9D%B4%EB%AF%80%EB%A1%9C%5C%5C%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cquad%20%5Cquad%20%3D%5Cfrac%20%7B%20%5Csqrt%20%7B%203%20%7D%5Csqrt%20%7B%20-1%20%7D%20%7D%7B%20-%5Csqrt%20%7B%202%20%7D%20%7D%3D-%5Csqrt%20%7B%20-%5Cfrac%20%7B%203%20%7D%7B%202%20%7D%20%7D%20$

종합하면

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※ 응용

(1)

$%5Cfrac%20%7B%20%5Csqrt%20%7B%20b%20%7D%20%7D%7B%20%5Csqrt%20%7B%20a%20%7D%20%7D%2B%5Csqrt%20%7B%20%5Cfrac%20%7B%20b%20%7D%7B%20a%20%7D%20%7D%3D0%EC%9D%B4%EB%9D%BC%EB%A9%B4%5Cquad%20%5Cfrac%20%7B%20%5Csqrt%20%7B%20b%20%7D%20%7D%7B%20%5Csqrt%20%7B%20a%20%7D%20%7D%3D-%5Csqrt%20%7B%20%5Cfrac%20%7B%20b%20%7D%7B%20a%20%7D%20%7D%EC%9D%B4%EB%AF%80%EB%A1%9C%5C%5C%20b%5Cge%200%EC%9D%B4%EA%B3%A0%2C%5Cquad%20a%3C0%EA%B0%80%5Cquad%20%EC%84%B1%EB%A6%BD%ED%95%9C%EB%8B%A4%EB%8A%94%5Cquad%20%EC%86%8C%EB%A6%AC%EC%9D%B4%EB%8B%A4.%5C%5C%20(b%5Cge%200%EC%9D%B8%5Cquad%20%EC%9D%B4%EC%9C%A0%EB%8A%94%5Cquad%20b%EA%B0%80%5Cquad%200%EC%9D%B4%EC%96%B4%EB%8F%84%5Cquad%200%3D0%EC%9C%BC%EB%A1%9C%5Cquad%20%EC%84%B1%EB%A6%BD%ED%95%98%EA%B8%B0%5Cquad%20%EB%95%8C%EB%AC%B8%EC%9D%B4%EB%8B%A4.)%20$

(2)

$%5Cfrac%20%7B%20%5Csqrt%20%7B%20x%20%7D%20%7D%7B%20%5Csqrt%20%7B%20x-1%20%7D%20%7D%3D-%5Csqrt%20%7B%20%5Cfrac%20%7B%20x%20%7D%7B%20x-1%20%7D%20%7D%5Cquad%20(x%5Cneq%200)%EB%9D%BC%EB%8A%94%5Cquad%20%EC%86%8C%EB%A6%AC%EB%8A%94%5Cquad%20x%5Cge%200%2C%5Cquad%20(x-1)%3C0%EC%9D%B4%EB%AF%80%EB%A1%9C%5C%5C%200%5Cle%20x%3C1%EC%9D%B8%EB%8D%B0%5Cquad%20x%5Cneq%200%EC%9D%B4%EB%AF%80%EB%A1%9C%5Cquad%200%3Cx%3C1%EC%9D%B4%EB%9D%BC%EB%8A%94%5Cquad%20%EB%9C%BB%EC%9D%B4%EB%8B%A4.%5C%5C%20%EC%A7%80%EC%88%98%EB%A1%9C%EA%B7%B8%EC%97%90%EC%84%9C%5Cquad%20%EA%B0%80%EB%81%94%5Cquad%20%ED%99%9C%EC%9A%A9%EB%90%98%EA%B8%B0%EB%8F%84%5Cquad%20%ED%95%9C%EB%8B%A4.%20$

2. 곱꼴의 루트

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종합하면

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[출처] 제2강 수와 식 Ι - (3) 루트를 이용한 간접조건|작성자 SperoSpera

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현재글 루트를 이용한 간접조건

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