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Take $ x = y $: - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 2l + 2w = 100 \Rightarrow l + w = 50

📌 The area is $ A = lw $. Express $ w = 50 - l $, so:

📌 This is a quadratic in $ l $, opening downward, so maximum occurs at the vertex:

📌 l = \frac{50}{2} = 25 \Rightarrow w = 25

📌 Thus, the maximum area is:

📌 A = 25 \times 25 = \boxed{625}

📌 Question: A quantum diagnostic device uses a function $ f(u) = u\sqrt{u} - 5u + 6\sqrt{u} $. Find the sum of all real roots of the equation $ f(u) = 0 $, given that all roots are non-negative.

📌 Solution: Let $ x = \sqrt{u} $, so $ u = x^2 $, and the equation becomes:

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