How do you solve cos² x=cosx+2?

Question

The restrictions are 0≤x≤2π
I know the answer is π, but how do you get that?

Answer 1

 

re-arrange the equation to give (cos^2 x) - (cos x) - 2 = 0

substitute x for cos x

that gives you a quadratic x^2 - x - 2 = 0

therefore (x - 2)(x + 1) = 0
so x = 2 or x = -1

substituting back cos x gives:

cos x = 2 or cos x = -1

cos x cannot = 2 therefore the only solution is cos x = -1

therefore x = Pi (no other solutions will fit the limits given)

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