용어

평차 (평균으로부터의 편차):Semi-difference 또는 Half-difference 평균 직사각형,평차 직사각형

이차방정식 근의 성질을 분석하고 영어 용어를 탐색했다.

The user is asking about a quadratic equation and wants me to:

1. Explain this in English
2. Translate to Korean
3. Find the English word for "평차" (which appears to be the deviation from the mean)

Let me analyze the mathematics:

• Quadratic equation: x² - 20x + 91 = 0
• Solutions: 7 and 13
• Sum of roots: 20 = 7 + 13
• Product of roots: 91 = 7 × 13
• Average of the two roots: (7 + 13)/2 = 20/2 = 10
• 평차 (deviation from mean): |10 - 7| = 3, |13 - 10| = 3
• This can also be calculated as: √(10² - 91) = √9 = 3

The term "평차" refers to the deviation of each root from their average. In English, this could be called:

• "semi-difference" (half the difference between the two roots)
• "deviation from mean"
• "distance from average"

In the context of quadratic equations, the most appropriate term would be "semi-difference" or "half-difference" because:

• The difference between the roots is: 13 - 7 = 6
• Half of this difference is: 6/2 = 3
• This is the distance from the average (10) to each root

Let me provide both English explanation and Korean translation.

English Explanation

Quadratic Equation Analysis: x² - 20x + 91 = 0

Solutions: 7 and 13

Vieta's Formulas:

• Sum of roots: 20 = 7 + 13
• Product of roots: 91 = 7 × 13

Average (Mean) of the two roots: Average = (7 + 13)/2 = 20/2 = 10

Semi-difference (deviation from mean):

• From the first root: 10 - 7 = 3
• From the second root: 13 - 10 = 3

Alternative calculation: Semi-difference = √(10² - 91) = √9 = 3

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한글 해석

2차 방정식 분석: x² - 20x + 91 = 0

해: 7과 13

근과 계수의 관계:

• 두 근의 합: 20 = 7 + 13
• 두 근의 곱: 91 = 7 × 13

두 근의 평균: 평균 = (7 + 13)/2 = 20/2 = 10

평차 (평균으로부터의 편차):

• 첫 번째 근으로부터: 10 - 7 = 3
• 두 번째 근으로부터: 13 - 10 = 3

대안 계산법: 평차 = √(10² - 91) = √9 = 3

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평차에 해당하는 영어 단어:

"Semi-difference" 또는 "Half-difference"

다른 표현들:

• Deviation from mean (평균으로부터의 편차)
• Distance from average (평균으로부터의 거리)

2차 방정식의 맥락에서는 **"semi-difference"**가 가장 정확한 수학 용어입니다.

 

https://claude.ai/chat/db024c27-a36d-4f71-8360-e9db43238047

 

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