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Home » Simplifions \( f(x) \) : - Rice University

Simplifions \( f(x) \) : - Rice University

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 2x^2 + 8 = 2x^2 - 8.

📌 Subtract \( 2x^2 \):

📌 a contradiction. Hence, no real solution exists. The equation is undefined at \( x = \pm 2 \), and there is no \( x \) satisfying the equation.

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

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

📌 v^2 \cdot v - 5v^2 + 6v = 0 \quad \Rightarrow \quad v^3 - 5v^2 + 6v = 0.

📌 v(v^2 - 5v + 6) = 0.

📌 Factor quadratic:

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