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t^2 - 4t + 3 = 0 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Compute the sum of the roots of the equation
\[ u\sqrt{u} - 5u + 6\sqrt{u} - 4 = 0 \]
given that all roots are non-negative real numbers.
Let \( x = \sqrt{u} \), so \( u = x^2 \) and \( u\sqrt{u} = x^2 \cdot...
\[ x^3 - 5x^2 + 6x - 4 = 0 \]
We solve this cubic equation. Try rational roots: \( \pm1, \pm2, \pm4...
Test \( x = 1 \):
\( 1 - 5 + 6 - 4 = -2
Test \( x = 2 \):
\( 8 - 20 + 24 - 4 = 8

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