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Home » The Secret to the Perfect Anniversary Gift? These Bands Are Selling Like Hotcakes! - Appcentric

The Secret to the Perfect Anniversary Gift? These Bands Are Selling Like Hotcakes! - Appcentric

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 نعوض $y = a - x$ في $y + z = a$:

📌 a - x + z = a \quad \Rightarrow \quad z = x

📌 نعوض $z = x$ و $y = a - x$ في $x^2 + y^2 + z^2 = 2a^2$:

📌 x^2 + (a - x)^2 + x^2 = 2a^2 \quad \Rightarrow \quad x^2 + a^2 - 2ax + x^2 + x^2 = 2a^2 \quad \Rightarrow \quad 3x^2 - 2ax + a^2 = 2a^2 \quad \Rightarrow \quad 3x^2 - 2ax - a^2 = 0

📌 x = \frac{2a \pm \sqrt{4a^2 + 12a^2}}{6} = \frac{2a \pm 4a}{6} \quad \Rightarrow \quad x = a \quad \text{أو} \quad x = -\frac{a}{3}

📌 بما أن $x$ يجب أن يكون عددًا صحيحًا، فإن $x = a$، وبالتالي $y = 0$ و $z = a$. لذلك، إحداثيات الرأس الرابع هي:

📌 \boxed{(a, 0, a)}

📌 السؤال: أوجد القيمة القصوى للتعبير $(\sin x + \cos x)^2

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a_2 = 3(2)^2 - 2(2) + 1 = 9
a_3 = 3(3)^2 - 2(3) + 1 = 22
a_4 = 3(4)^2 - 2(4) + 1 = 41
a_5 = 3(5)^2 - 2(5) + 1 = 66
Sum of the first 5 terms:
+ 9 + 22 + 41 + 66 = 140
A rectangular prism has dimensions 4 cm, 5 cm, and 6 cm. If the dimens...
\times 5 \times 6 = 120 \text{ cubic centimeters}
New dimensions are \( 8 \), \( 10 \), and \( 12 \).
\times 10 \times 12 = 960 \text{ cubic centimeters}

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