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Home » \( f(3) = a(3)^3 + b(3)^2 + c(3) + d = 2 \), which simplifies to: - Dachbleche24

\( f(3) = a(3)^3 + b(3)^2 + c(3) + d = 2 \), which simplifies to: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \log_2((x+3)(x-1)) = 3 \implies (x+3)(x-1) = 2^3 = 8

📌 Développez et résolvez : \(x^2 + 2x - 3 = 8 \implies x^2 + 2x - 11 = 0\).

📌 Utilisez la formule quadratique : \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2} = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}\).

📌 Puisque \(x > 1\) (pour que les logarithmes soient définis), \(x = -1 + 2\sqrt{3}\).

📌 #### \(-1 + 2\sqrt{3}\)

📌 Une suite géométrique a un premier terme de 3 et une raison commune de 2. Quelle est la somme des 5 premiers termes ?

📌 La somme \(S_n\) des \(n\) premiers termes d’une suite géométrique est \(S_n = a \frac{r^n - 1}{r - 1}\).

📌 Ici, \(a = 3\), \(r = 2\), \(n = 5\).

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