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Home » Thus, the sum of all real solutions is $ \boxed13 $. - Londonproperty

Thus, the sum of all real solutions is $ \boxed13 $. - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 g'(u) = 6u - 16u^3 = 2u(3 - 8u^2)

📌 Set $ g'(u) = 0 $: $ u = 0 $ or $ 3 - 8u^2 = 0 \Rightarrow u^2 = rac{3}{8} \Rightarrow u = \pm \sqrt{rac{3}{8}} = \pm rac{\sqrt{6}}{4} $

📌 Evaluate $ g(u) $:

📌 At $ u = 0 $: $ g = 0 $

📌 At $ u = \pm rac{\sqrt{6}}{4} $:

📌 g = 3\left(rac{6}{16}

📌 ight) - 4\left(rac{36}{256}

📌 ight) = rac{18}{16} - rac{144}{256} = rac{9}{8} - rac{9}{16} = rac{18 - 9}{16} = rac{9}{16} = 0.5625

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