Question

solve on the interval [0, 2pi).

2cos^2(x)-3cos(x)+1=0

Answer 1

Question #9915

Solve on the interval [0, 2pi): 2cos^2(x) - 3cos(x) + 1 = 0

Solution

$$2 \cos^ {2} x - 3 \cos x + 1 = 0$$ $$\cos x = t;$$ $$t \in [ - 1; 1 ]$$ $$2 t ^ {2} - 3 t + 1 = 0$$ $$D = 1; \sqrt {D} = 1;$$ $$t _ {1} = 1; t _ {2} = \frac {1}{2};$$ $$\left\{ \begin{array}{l} \cos x = 1 \\ \cos x = \frac {1}{2} \end{array} \right.$$ $$x _ {1} = 0;$$ $$x _ {2} = \frac {\pi}{3}.$$

Answer: $x_{1} = 0, x_{2} = \frac{\pi}{3}$ .