Question

x+1/x=√3 ,x³⁰+x²⁴+x¹⁸+x¹²+x⁶+1= fine this value and explain​

Answer 1

ANSWer

NECCHE TO DEKHO ..ARE NEECHE

and we're given to find the value of

x^{30}+x^{24}+x^{18}+x^{12}+x^6+1x

30 +x 24 +x 18 +x 12 +x 6 +1

First consider the given equation.

x+\dfrac {1}{x}=\sqrt3x+

x1 = 3

Taking the cubes of both the sides,

\begin{gathered}\left (x+\dfrac {1}{x}\right)^3=\left(\sqrt3\right)^3\\\\\\x^3+3x+\dfrac {3}{x}+\dfrac {1}{x^3}=3\sqrt3\\\\\\x^3+\dfrac {1}{x^3}+3\left (x+\dfrac {1}{x}\right)=3\sqrt 3\\\\\\x^3+\dfrac {1}{x^3}+3\sqrt 3=3\sqrt 3\\\\\\x^3+\dfrac {1}{x^3}=0\\\\\\\dfrac {x^6+1}{x^3}=0\\\\\\x^6+1=0\\\\\\x^6=-1\end{gathered}

(x+ x1 ) 3×( 3 ) 3 x 3 +3x+ x 3 + x 31 =3

3x 3+x 31 +3(x+ x1 )=3 3x 3 + x 31 +33 =3 3 x 3 + x 1 =0x 3x 6 +1

=0x 6 +1=0x 6=−1

Then,

\begin{gathered}x^{30}+x^{24}+x^{18}+x^{12}+x^6+1\\\\=(x^6)^5+(x^6)^4+(x^6)^3+(x^6)^2+x^6+1\\\\=(-1)^5+(-1)^4+(-1)^3+(-1)^2+-1+1\\\\=-1+1-1+1-1+1\\\\=\mathbf {0}\end{gathered}

x 30 +x 24 +x 18 +x 12 +x 6 +1=(x 6 ) 5 +(x 6 ) 4 +(x 6 ) 3 +(x 6 ) 2 +x 6 +1

=(−1) 5 +(−1) 4 +(−1) 3 +(−1) 2 +−1+1=−1+1−1+1−1+1=0

Answer 2

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Anyway Hello