SOLUTION: Find the solutions of the equation that are in the interval [0, 2*Pi); separate your answers with commas. - 2cos 2(x)+ cos(x)+ 1 = 0; I already found 2Pi/3 and 4Pi/3 as answers

Question 183369This question is from textbook
: Find the solutions of the equation that are in the interval [0, 2*Pi); separate your answers with commas.
- 2cos 2(x)+ cos(x)+ 1 = 0;
I already found 2Pi/3 and 4Pi/3 as answers and they came up correct but the system says there are more. I am having trouble finding the others. Any help would be greatly appreciated. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Notice how the term "cos(x)" is used most in this equation. So let

Plug in

Factor the left side.

or Set each factor equal to zero

Now let's solve each individual equation

------------------------------

Start with the first equation

Plug in

Isolate the term "cos(x)"

or Solve for "x". Since we're only concerned about the interval [

), this means that there are only two solutions.

------------------------------

Move onto the next equation

Plug in

Add 1 to both sides.

Solve for "x". Note: because we're limited to the interval [

), there's only one solution

===============================

Answer:

So on the interval [

), we have the three solutions: , or
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