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(1-x^3)/(1-x)=0\implies x^3=1`

Then for any
`n`, we have

`x^(3n)=(x^3)^n=1^n=1`