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Yasmin Camacho

Yasmin Camacho

Answered question

2022-05-22

Prove that cos ( π / 7 ) is root of equation 8 x 3 4 x 2 4 x + 1 = 0

Answer & Explanation

rass1k6s

rass1k6s

Beginner2022-05-23Added 13 answers

Put 2 x = z + 1 z in
( 2 x ) 3 ( 2 x ) 2 2 ( 2 x ) + 1 = 0
and multiply by z+1 to find z 7 + 1 = 0 whose roots are are e ( 2 k + 1 ) π i / 7 where k 0 , ± 1 , ± 2 , ± 3 ( mod 7 )
So, the roots of
z 7 + 1 z + 1 = 0
are e ( 2 k + 1 ) π i / 7 where k 0 , ± 1 , ± 2 , 3 ( mod 7 )
Finally 2 cos y = e i y + e i y

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