Question Number 148890 by mathdanisur last updated on 01/Aug/21

if x + (1/x) = (√3) find x^(18) + x^(12) + x^6 + 1 = ?

Answered by nimnim last updated on 01/Aug/21

x+(1/x)=(√3)⇒x^2 +(1/x^2 )=1 ⇒x^6 +(1/x^6 )+3x^2 .(1/x^2 )(x^2 +(1/x^2 ))=1⇒x^6 +(1/x^6 )=−2 ⇒x^(12) +2x^6 +1=0 ⇒(x^6 +1)^2 =0 ⇒ x^6 =−1 Now, x^(18) +x^(12) +x^6 +1=(−1)^3 +(−1)^2 −1+1 =−1+1−1+1 =0 ★

Commented bymathdanisur last updated on 01/Aug/21

Thank you Ser