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Home » أولاً، نحول 3 إلى كسر بمقام 4: - NBX Soluciones

أولاً، نحول 3 إلى كسر بمقام 4: - NBX Soluciones

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 استخدم الصيغة التربيعية: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

📌 هنا، \(a = 2\)، \(b = -4\)، \(c = -6\)

📌 المميز: \((-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64\)

📌 الجذور: \(x = \frac{4 \pm \sqrt{64}}{4} = \frac{4 \pm 8}{4}\)

📌 \(x_1 = \frac{12}{4} = 3\)

📌 \(x_2 = \frac{-4}{4} = -1\)

📌 #### الجذور = 3، -1

📌 خزان مملوء بـ 800 لتر من الماء. يتم تصريف الماء بمعدل 50 لترًا في الساعة، وفي الوقت نفسه، يتم إضافة الماء بمعدل 30 لترًا في الساعة. كم ساعة يستغرق إفراغ الخزان؟

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\[ (5a + b) - (3a + b) = 2 - 1 \]
\[ 2a = 1 \]
\[ a = \frac{1}{2} \]
Substitute \(a = \frac{1}{2}\) into Equation 4:
\[ 3\left(\frac{1}{2}\right) + b = 1 \]
\[ \frac{3}{2} + b = 1 \]
\[ b = 1 - \frac{3}{2} = -\frac{1}{2} \]
Substitute \(a = \frac{1}{2}\) and \(b = -\frac{1}{2}\) into Equation...
\[ \frac{1}{2} - \frac{1}{2} + c = 2 \]
\[ c = 2 \]

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Solution: Let the four terms be $ a - \frac{3d}{2},\ a - \frac{d}{2},\...
\left(a - \frac{3d}{2}\right)^2 + \left(a + \frac{3d}{2}\right)^2 = 2a...
The sum of all four terms is:
The square of the sum is $ (4a)^2 = 16a^2 $.
2a^2 + \frac{9d^2}{2} = 16a^2
\Rightarrow \frac{9d^2}{2} = 14a^2

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