Question

Solve, cos 2x + 2cosx - 3=0, if 0 12 years ago

Answer 1

I came up with x=0+2kpi?

Answer 2

use the identity
cos 2s = 2cos^2 x - 1

Answer 3

* cos 2x

Answer 4

(x+3)(x-1)=0
cos x=-3
cosx=-1
x=0+2kpi

Answer 5

perhaps I am doing it incorrectly

Answer 6

substituting
2cos^2 x - 1 + 2 cos x - 3 = 0
2cos^2 x + 2 cos x - 4 = 0
(2 cos x + 4 )( cos x - 1) = 0

cos x = 1

Answer 7

so between 0 and 2 pi...

Answer 8

well no solution if its if 0<x<2pi

but 0 , 2pi if we use if 0=<x<=2pi

Answer 9

ah, ok, thanks

Answer 10

yw

Answer 11

We have cosinuses of 3 values added together ( 2x,x,x) and every single one of them is not bigger then 1 and suming up they are equals to 3( cos2x+2cosx-3=0 <=> cos2x +2cos=3) means they are all equal 1, since if even one of them were lower then one this equasion would make no sense. Thus cos2x=cosx=1, and it is only correct if x=0. Hope i helped. I believe that this reasoning is easier then the one of precursor, as it does not require counting only noticing that cosa is never bigger then 1 no matter the a .