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what happens when a dog eats chocolate - Sourci

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Question: Compute the sum of the roots of the equation \( v\sqrt{v} - 5v + 6\sqrt{v} = 0 \), given that all roots are non-negative real numbers.

📌 Solution: Let \( u = \sqrt{v} \), so \( v = u^2 \), and \( u \geq 0 \). Substitute:

📌 u^2 \cdot u - 5u^2 + 6u = 0 \Rightarrow u^3 - 5u^2 + 6u = 0

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

📌 \( u = 0 \Rightarrow v = 0 \)

📌 \( u = 2 \Rightarrow v = 4 \)

📌 \( u = 3 \Rightarrow v = 9 \)

📌 All roots are non-negative, so valid. The sum of the roots is \( 0 + 4 + 9 = 13 \).

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