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Home » إذن، القيمة التقريبية لـ \( n \) هي: - Baxtercollege

إذن، القيمة التقريبية لـ \( n \) هي: - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 No: for each factorization, we get a point. But since \(m\) and \(n\) are determined, and \(x = m+n\), \(y = n-m\), and since \(m\) runs through all 16 divisors (positive and negative), we get 16 values of \(x\), 16 of \(y\), but not necessarily distinct points.

📌 But each pair \((m,n)\) with \(mn = 506\) gives a unique \((x,y)\)?

📌 Suppose \((m,n)\) and \((m',n')\) give same \((x,y)\): then \(m + n = m' + n'\) and \(n - m = y\).

📌 From second: \(n = m + y\), substitute: \(m(m + y) = 506\), and \(m(n') = m'(m + y)\). But complicated.

📌 Instead, note that \(x = m + n\), \(y = n - m\), so \(x^2 - y^2 = (m+n)^2 - (n - m)^2 = 4mn = 4 \cdot 506 = 2024\), so every such pair satisfies the equation.

📌 And different \((m,n)\) may give same \((x,y)\)?

📌 Suppose \((m_1, n_1)\) and \((m_2, n_2)\) give same \((x,y)\):

📌 Then \(m_1 + n_1 = m_2 + n_2\) and \(n_1 - m_1 = y\).

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