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Home » GCD(18,42) = 6 - Malaeb

GCD(18,42) = 6 - Malaeb

📅 May 3, 2026 👤 scraface

May 03, 2026

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\frac{1}{\sqrt{n} + \sqrt{n+1}} \cdot \frac{\sqrt{n+1} - \sqrt{n}}{\sq...
\sum_{n=1}^{50} \left( \sqrt{n+1} - \sqrt{n} \right) = (\sqrt{2} - \sq...
\sqrt{51} - \sqrt{1} = \sqrt{51} - 1
Therefore, the sum is \( \boxed{\sqrt{51} - 1} \).
Question: Find the quadratic polynomial \( f(x) \) such that \( f(0) =...
Solution: Let \( f(x) = ax^2 + bx + c \). Use the given conditions:
\( f(0) = c = 4 \)
\( f(1) = a + b + c = 1 \) → \( a + b + 4 = 1 \) → \( a + b = -3 \)
\( f(2) = 4a + 2b + c = -4 \) → \( 4a + 2b + 4 = -4 \) → \( 4a + 2b =...
a + b = -3 \\

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c = \frac{a + b - z}{2}, \quad A = \frac{1}{2}ab = \frac{(a + b)^2 - z...
Alternatively, recall that \( A = r s = c s \), so:
\frac{\pi c^2}{A} = \frac{\pi c^2}{c s} = \frac{\pi c}{s}.
But we need a closed-form expression in terms of \( z \) and \( c \)....
In a right triangle, \( r = \frac{a + b - c}{2} \), and \( c = \text{h...
Actually, a cleaner approach:
Let the triangle have legs \( a, b \), hypotenuse \( z \). Then:
A = \frac{ab}{2}, \quad s = \frac{a + b + z}{2}, \quad r = \frac{a +
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