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Home » Equation: \( x^2 + (x+1)^2 = 145 \) - AMAZONAWS

Equation: \( x^2 + (x+1)^2 = 145 \) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Thus, $\phi(48) = \boxed{16}$.
Question: A cartographer detects a triangular layout of ancient ruins...
Solution: Let the sides be $a-1$, $a$, $a+1$. This is a triangle only...
$(a-1) + a > a+1 \Rightarrow 2a - 1 > a + 1 \Rightarrow a > 2$.
Use Heron’s formula. Let $s = \frac{(a-1) + a + (a+1)}{2} = \frac{3a}{...
Then area $A = \sqrt{s(s - a+1)(s - a)(s - a-1)} = \sqrt{ \frac{3a}{2}...
= \sqrt{ \frac{3a}{2} \cdot \left(\frac{a}{2} + 1\right) \cdot \left(\...
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