Ward Nichols
01/27/2024 · High School

3. Déduis-en la solution de \( \left(E_{1}\right) \) tel que : \( \forall x \in\left[0 ; 2 \pi\left[,-4 \cos ^{2} x+2(\sqrt{3}-\sqrt{2}) \cos x-\sqrt{6}=0\right.\right. \)

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Pour résoudre l'équation \( E_1 : -4 \cos^2 x + 2(\sqrt{3} - \sqrt{2}) \cos x - \sqrt{6} = 0 \), on pose \( y = \cos x \) et obtient une équation quadratique en \( y \). On utilise la formule quadratique pour trouver les solutions de \( y \) et ensuite, on trouve les valeurs de \( x \) dans l'intervalle \([0, 2\pi[\) en utilisant \( x = \arccos(y) \) et \( x = 2\pi - \arccos(y) \).

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