Find all the values of x in the interval 0

Question

Find all the values of x in the interval 0<=x<360 that satisfy 3cos2x=cosx+2

dtan5457 · Answer

So I have 3cos2x-cosx-2=0

now im not sure

dtan5457 · Answer

@sleepyjess

sleepyjess · Answer

@Kainui

dtan5457 · Answer

once it's factored it easy..but not sure how to do here.

if i substitute cos(x)=u, i still don't see how it could work here

dtan5457 · Answer

this is more than likely gonna turn to a quadratic somehow..

mathslover · Answer

Hmm!

mathslover · Answer

$3\cos 2x = \cos x + 2 $ 

Put $\cos2x = 2\cos^2x - 1$ 

$3(2\cos^2 x - 1) = \cos x + 2$

You get : 

$6 \cos^2 x - cos x - 5 = 0 $

mathslover · Answer

Use quadratic equation to solve for cos x.

dtan5457 · Answer

How did you know what to substitute? @mathslover

mathslover · Answer

Did you mean by the formula? Well, it is pretty clear that we can solve it by quadratic equation but for that we need degree of the polynomial = 2 

And since, cos 2x can be simplified into $\cos^2 x$ ... with the formula : $$ \cos 2x = 2\cos^2 x - 1$$ 

So, I just used it!

mathslover · Answer

Once you start solving such type of questions, you will get used to these techniques! Don't worry.. just keep practicing!