Grade 12th passAlgebra
If x + 1/x = √3.then find x100 + 1/x100.what is the solution
5 Answers
Vikas TU
x + 1/x = √3
squaring both sides,
x^2 + 1/x^2 = √3 – 2
again squaring,
x^4 + 1/x^4 = (√3-2)^2 -2
.
.
Go on like this on series for up till x^100 + 1/x^100
krunal
assume that x=w {where w is complex cube root of unity}
the substitute x=w in given equation and mark it as equ.
then w^100 +1/w^100.
since w^3 =1....we can write w^100 as w^99.w^1= w^1
and by substituting u get ans,
PASUPULETI GURU MAHESH
x+1/x=√3 you consider x=cos(teeta)+i sin(teeta)
then substitute teeta = 30 degrees
then x100+1/x100=cos(100 teeta) by the complex number concept
= cos (3000)
= -1/2
thank you
Mosaraf Mondal
x+1/x=√3 you consider x=cos(teeta)+i sin(teeta) then substitute teeta = 30 degrees then x100+1/x100=2 ×cos(100 teeta) by the complex number concept = 2×cos (3000) = 2×(-1/2 ) = -1
yifs
x+1/x=√3
(x+1/x)2=3
x2+2+1/(x2)=3
x2-1+1/(x2)=0
(x+1/x)(x2-1+1/(x2))=0
x3+1/(x3)=0
(x3+1/(x3))∑n=016(((x3)16-n)((-1/(x3))n))=0
(x3)17+(1/(x3))17=0
x51+1/(x51)=0
(x51+1/(x51))(x49+1/(x49))=0
x100+x2+1/(x2)+1/(x100)=x2-1+1/(x2)
x100+1/(x100)=-1
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