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Home » #### \(x = 3\) أو \(x = 1\) - Simpleprint

#### \(x = 3\) أو \(x = 1\) - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Final answer: $ \boxed{30 - 12\sqrt{6}} $

📌 Question: Rationalize the denominator of $ \frac{5}{\sqrt{7} + \sqrt{2}} $.

📌 Multiply numerator and denominator by the conjugate $ \sqrt{7} - \sqrt{2} $:

📌 \frac{5}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}} = \frac{5(\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})}

📌 Simplify the denominator using the difference of squares:

📌 \frac{5(\sqrt{7} - \sqrt{2})}{5} = \sqrt{7} - \sqrt{2}

📌 Final answer: $ \boxed{\sqrt{7} - \sqrt{2}} $

📌 Question: Expand the product $ (x^2 + 2x + 3)(x^2 - 2x + 3) $.

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r = \frac{5\sqrt{2}}{2}
C = 2\pi r = 2\pi \left(\frac{5\sqrt{2}}{2}\right) = 5\pi\sqrt{2}
Thus, the circumference of the circle is:
\boxed{5\pi\sqrt{2}}
Given a triangle with sides \(7 \, \text{cm}\), \(24 \, \text{cm}\), a...
The triangle is a right triangle (since \(7^2 + 24^2 = 25^2\)). The ar...
A = \frac{1}{2} \times 7 \times 24 = 84 \, \text{cm}^2
The altitude to the hypotenuse \(c = 25\) is:
h_c = \frac{2A}{c} = \frac{168}{25} = 6.72 \, \text{cm}
The altitude to side \(a = 7\)

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