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baltimore marriott inner harbor at camden yards - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Solution: Let $ \sqrt{u} = t $, so $ u = t^2 $. Substituting into the equation:

📌 t^2 \cdot t - 6t^2 + 7t - 12 = 0 \Rightarrow t^3 - 6t^2 + 7t - 12 = 0

📌 We are now to find the sum of the roots of the cubic equation

📌 t^3 - 6t^2 + 7t - 12 = 0

📌 By **Vieta’s Formula**, the sum of the roots is the coefficient of $ t^2 $ with the opposite sign:

📌 \text{Sum of roots} = 6

📌 Since $ t = \sqrt{u} \geq 0 $, and all roots are real and non-negative, each root $ t $ corresponds to a non-negative $ u = t^2 $. Therefore, the sum of the values of $ u $ is not directly the sum of $ t^2 $, but the question asks for the **sum of the roots of the original equation in $ u $**, which are $ t^2 $, so we compute:

📌 \sum u = \sum t^2

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