Question

Решите уравнение СРОЧНОООООО
2cos^2x-3cosx+1=0

Answer 1

Решение во вложении.

Answer 2

$2Cos^{2}x-3Cosx+1=0\\\\Cosx=m \ , \ -1\leq m\leq1\\\\2m^{2}-3m+1=0\\\\D=(-3)^{2}-4\cdot 2\cdot 1=9-8=1\\\\m_{1} =\dfrac{3-1}{4} =\frac{1}{2} \\\\m_{2}=\dfrac{3+1}{4}=1\\\\\\\left[\begin{array}{ccc}Cosx=\dfrac{1}{2} \\Cosx=1\end{array}\right\\\\\\\left[\begin{array}{ccc}x=\pm arc Cos\dfrac{1}{2}+2\pi n,n\in Z \\x=2\pi n,n\in Z \end{array}\right\\\\\\ \left[\begin{array}{ccc}x=\pm \dfrac{\pi }{3}+2\pi n,n\in Z \\x=2\pi n,n\in Z \end{array}\right$