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Home » Simplify: \(120v + 2400 + 180v = 5v^2 + 100v\). - Deep Underground Poetry

Simplify: \(120v + 2400 + 180v = 5v^2 + 100v\). - Deep Underground Poetry

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 v(v^2 - 5v + 6) = 0.

📌 Factor quadratic:

📌 v(v - 2)(v - 3) = 0.

📌 So, \( v = 0, 2, 3 \). Since \( u = v^2 \), the corresponding roots are:

📌 All roots are non-negative, so valid.

📌 Sum of roots: \( 0 + 4 + 9 = 13 \).

📌 Define \( M(u) = u - \frac{u^4}{4} \) for all real \( u \). If \( n \) is a positive integer, define \( b_n \) by \( b_1 = 1 \) and \( b_{n} = M(b_{n-1}) \) for \( n \geq 2 \). Compute \( b_3 \).

📌 We compute recursively:

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