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sin54-10-x-1-x-1-is-root-ax-2-bx-c-0-a-b-c-is-integer-a-




Question Number 182854 by manxsol last updated on 16/Dec/22
(sin54)^(10) =x_1     x_(1  ) is root  ax^2 +bx+c=0    a,b,c   is integer  a=?
(sin54)10=x1x1isrootax2+bx+c=0a,b,cisintegera=?
Commented by manxsol last updated on 16/Dec/22
ok,I will correct it., thanks   for the suggestion.  How did?you do it?
ok,Iwillcorrectit.,thanksforthesuggestion.Howdid?youdoit?
Commented by Frix last updated on 15/Dec/22
???  a=1    (x−x_1 )(x−x_2 )=x^2 −(x_1 +x_2 )x+x_1 x_2   b=−(x_1 +x_2 )  c=x_1 x_2
???a=1(xx1)(xx2)=x2(x1+x2)x+x1x2b=(x1+x2)c=x1x2
Commented by manxsol last updated on 15/Dec/22
sorry, i am edit problem
sorry,iameditproblem
Commented by manxsol last updated on 15/Dec/22
thanks
thanks
Commented by Frix last updated on 15/Dec/22
No need to be sorry.    sin 54° =((1+(√5))/4)  sin^(10)  54° =((123+55(√5))/(2048))
Noneedtobesorry.sin54°=1+54sin1054°=123+5552048
Commented by manxsol last updated on 15/Dec/22
  I solved it like this  sin54=(((√5)+1)/4)=(1/2) (((√5)+1)/2)=(1/2)Φ  ((1/2))^(10) Φ^(10) =(1/(1024)) (((123+55(√5))/2))  =((123+55(√5))/(2048))=x_1   See (★)^   roots integer⇒x_(2 conjugate)   x_2 =((123−55(√5))/(2048))  x_1 +x_2 =((246)/(2048))  x_1 x_2 =(4/(4194304))  calculate  using editor tinku tara  2048^2   4194304.0  123^2 −5×55^2   4.0  246×2048  503808.0  4194304/4  1048576.0  503808/4  125952.0  input   4×5  [push]   enter  [push]   ⋮  [push]   calcular  20.0      x^2 −((246)/(2048))x+(4/(4194304))=0  4194304x^2 −503808x+4=0  1048576x^2 −125952x+1=0  solution:  a=1048576      (★)  Φ^(10) =(((1+(√5))/2))^(10)   =((123+55(√5))/2)  serie de fibonacci   determinant ((1,2,3,4,5,6,7,8,9,(10),(11)),(1,1,2,3,5,8,(13),(21),(34),(55),(89)))    a=55  b=123  deduccion hecha de tabla de  potencias de Φ=(1+(√5))/2
Isolveditlikethissin54=5+14=125+12=12Φ(12)10Φ10=11024(123+5552)=123+5552048=x1See()rootsintegerx2conjugatex2=1235552048x1+x2=2462048x1x2=44194304calculateusingeditortinkutara204824194304.012325×5524.0246×2048503808.04194304/41048576.0503808/4125952.0input4×5[push]enter[push][push]calcular20.0x22462048x+44194304=04194304x2503808x+4=01048576x2125952x+1=0solution:a=1048576()Φ10=(1+52)10=123+5552seriedefibonacci12345678910111123581321345589a=55b=123deduccionhechadetabladepotenciasdeΦ=(1+5)/2
Commented by Frix last updated on 15/Dec/22
You wrote a is integer.  You should have written a, b, c are integer.
Youwroteaisinteger.Youshouldhavewrittena,b,careinteger.

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