Răspuns:
D
Explicație pas cu pas:
[tex]2 \cos^{2} (x) - 11 \cos(x) + 5 = 0[/tex]
[tex] \cos(x) = t [/tex]
[tex]2 {t}^{2} - 11t + 5 = 0[/tex]
[tex](2t - 1)(t - 5) = 0[/tex]
[tex]t - 5 = 0 \implies t = 5 \\ \cos(x) = 5 > 1 \ \ \ fara \ \ solutii[/tex]
[tex]2t - 1 \implies t = \frac{1}{2} \\ \cos(x) = \frac{1}{2} [/tex]
[tex]x = \frac{\pi}{3} + 2k\pi \ \ ; \ \ x = \frac{5\pi}{3} + 2k\pi \\ [/tex]
[tex]x \in \Big\{ - \frac{\pi}{3} + 2k\pi \ \Big|k\in \mathbb{Z}\Big\} \cup \Big\{\frac{\pi}{3} + 2k\pi \ \Big|k\in \mathbb{Z}\Big\} \\ [/tex]
