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Home » So we seek $ \max(\sin 3x \sin x) $. Use identity: - Abu Waleed Tea

So we seek $ \max(\sin 3x \sin x) $. Use identity: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان م...
الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) =...
ثم $a + b = d(x + y) = 96$، لذا يجب أن يكون $d$ قاسمًا للعدد $96$.
لتعظيم $d$، نختار أكبر قاسم للعدد $96$ بحيث يكون $x + y$ عددًا صحيحًا...
أكبر قاسم للعدد $96$ هو $48$، مع $x + y = 2$. الزوج $(x, y) = (1, 1)$...
إذن، $a = 48 \cdot 1 = 48$، $b = 48 \cdot 1 = 48$، و$\gcd(a,b) = 48$.
لذلك، أكبر قيمة ممكنة لـ $\gcd(a,b)$ هي $\boxed{48}$.
السؤال: ما هو القاسم المشترك الأكبر للعددين $105$ و $165$؟
الحل: نطبق خوارزمية إقليدس لإيجاد $\gcd(105, 165)$.
= 1 \cdot 105 + 60

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