How to solve the cubic \(\displaystyle{x}^{{3}}-{3}{x}+{1}={0}\) This was

Pasegeabe85xy

Pasegeabe85xy

Answered question

2022-03-29

How to solve the cubic x33x+1=0
This was a multiple choice question with options being
(A)cos2π9,cos8π9,cos14π9
(B)2cos2π9,2cos8π9,2cos14π9
(C)cos2π11,cos8π11,cos14π11
(D)2cos2π11,2cos8π11,2cos14π11
I tried to eliminate options using the sum and product of roots but I can't figure out if
cos2π9+cos8π9+cos14π9=0
or
cos2π11+cos8π11+cos14π11=0

Answer & Explanation

membatas0v2v

membatas0v2v

Beginner2022-03-30Added 19 answers

Hint: (2cosθ)33(2cosθ)+1=2cos3θ+1
Cason Harmon

Cason Harmon

Beginner2022-03-31Added 8 answers

Put x=2t
Hence
8t36t+1=0
Now put t=cosθ Hence
2cos(3θ)=1
And the rest is simple trigonometric equation

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