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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Number of interior points (in unit triangular lattice): $ \frac{(n-2)(n-1)}{2} $ for $n \geq 2$. But this gives approximations.

📌 Alternatively, for a large equilateral triangle of side $n$ in a triangular lattice (where each small triangle has side 1), the number of lattice points strictly inside is:

📌 I = \frac{(n-1)(n-2)}{2}

📌 For $n = 6$:

📌 I = \frac{(6-1)(6-2)}{2} = \frac{5 \cdot 4}{2} = 10

📌 This formula arises from known results in triangular lattice geometry: the number of interior points in a triangle of side $n$ is $\frac{n(n-2)(n-1)}{6}$, or equivalently $\frac{(n-1)(n-2)}{2}$.

📌 Thus, the number of interior lattice points is $ \boxed{10} $.Question: Compute the sum of the roots of the equation

📌 u\sqrt{u} - 5u + 6\sqrt{u} = 0,

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