Question

If X²+ X + 1 =0 then the value of x ^3n is​

Answer 1

Recall that

$1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})$

So we have

$x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1$

Then for any $n$, we have

$x^{3n}=(x^3)^n=1^n=1$