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why do i sweat so easily - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5Question: If a climate model predicts temperature changes over time with the equation $ u\sqrt{u} - 5u + 6\sqrt{u} = 0 $, find the sum of all real roots of the equation.

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

📌 Factoring out $ x $:

📌 So the solutions for $ x $ are $ x = 0, 2, 3 $. Since $ x = \sqrt{u} $, we find the corresponding $ u $ values:

📌 The real roots of the original equation are $ u = 0, 4, 9 $. Their sum is:

📌 Question: A renewable energy system’s efficiency is modeled by the equation $ \frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2 $. Find $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.

📌 Solution: Let $ x = \frac{a + 2b}{a - 2b} $. Then the equation becomes:

📌 x + \frac{1}{x} = 2

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