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Home » Taking the positive solution: \( n = \frac402 = 20 \). - 500apps

Taking the positive solution: \( n = \frac402 = 20 \). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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Question: Compute the sum of the roots of the equation \( v\sqrt{v} -...
Solution: Let \( u = \sqrt{v} \), so \( v = u^2 \), and \( u \geq 0 \)...
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...
\( u = 0 \Rightarrow v = 0 \)
\( u = 2 \Rightarrow v = 4 \)
\( u = 3 \Rightarrow v = 9 \)
All roots are non-negative, so valid. The sum of the roots is \( 0 + 4...
Thus, the sum is \( \boxed{13} \).
Question: Let \( x, y, z \) be positive real numbers such that \( x +...

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