Question Number 148155 by Khalmohmmad last updated on 25/Jul/21

Answered by Rasheed.Sindhi last updated on 26/Jul/21

x+(1/x)=−1⇒x^2 +x+1=0  x=ω,ω^2   x=ω  x^(1400) +x^(1363) +x^(37)   =ω^(1400) +ω^(1363) +ω^(37)   =ω^(1400 mod 3) +ω^(1363 mod 3) +ω^(37 mod 3)   =ω^2 +ω+ω=−1+ω  x=ω^2   =(ω^2 )^2 +ω^2 +ω^2   =ω.ω^3 +ω^2 +ω^2   =ω+ω^2 +ω^2   =−1+ω^2