+333 x+1/x=√3 (Let us assume this one as a+b form)
a^2+b^2 = (a+b)^2–2ab ( apply this formula in above)
x^2+1/x^2=1
We know that
a^3+b^3= (a+b)(a^2-ab+b^2)
Now => x^3+1/x^3= 0
x^6=-1 ==> x^6+1=0
Coming to the question…
x^18+x^12+x^6+1
x^12(x^6+1)+1(x^6+1) = 0 (since above equation x^6+1=0)
Final answer=zero.
