Question

Solve on the interval [0,27): RCŨsx+c05X +1 = ] T O 3 A. X= 27,x = x=57 4. 4 O B. X = 27,X = O c. X= 7T,X = 1 47T 3 T D. X= ET 6 6 NAMAN

Answer 1

C.

`x=\pi,x=(2\pi)/(3),x=(4\pi)/(3)`

Explanation:

We have the following function:

`2cos^2x+3cosx\: +1\: =\: 0`

Using the substitution method, we can calculate the value of x, like this:

`\begin{gathered} u=\cos x \\ \text{ therefore:} \\ 2u^2+3u+1=0 \\ 3u=2u+u \\ 2u^2+2u+u+1=0 \\ 2u(u+1)+u+1=0 \\ (u+1)(2u+1)=0 \\ u+1=0\rightarrow u=-1 \\ 2u+1=0\rightarrow2u=-1\rightarrow u=-(1)/(2) \\ \text{ replacing:} \\ \cos x=-1\rightarrow x=\cos ^(-1)(-1)\rightarrow x=\pi \\ \cos x=-(1)/(2)\rightarrow x=\cos ^(-1)(-(1)/(2))\rightarrow x=(2\pi)/(3),(4\pi)/(3) \end{gathered}`