Square root(cosx) +2cosx-1

Question

trying to solve each equation for all values of x

Answer 1

If you meant to set the equation equal to zero, solve it as such:

 

SQRT(cos x) + 2cos x -1 = 0

 

SQRT(cos x) = 1 - 2cos x

 

cos x = 1 - 4cos x + 4cos² x

 

4cos² x -5cos x + 1 = 0 and solve it as a quadratic using substitution (let cos x = x)

 

4x² -5x + 1 = 0  use the quadratic equation

 

[5+/- 2sqrt(2)]/8  and substitute cos x for x in your 2 factors and get:

 

(cos x - [5+2sqrt(2)]/8) (cos x - [5-2sqrt(2)]/8) and use Invcos to find the values of x