Question 66
If $$x^2 + x + 1 = 0$$, then $$x^{2018} + x^{2019}$$ equals which of the following:
Solution
We know that,
$$x^{3} - 1 = (x - 1)(x^{2} + x + 1)$$
Since, $$x^2 + x + 1 = 0$$
$$\therefore $$ $$x^{3} - 1$$ = 0
=> $$x^{3}$$ = 1
Now, $$x^{2018} + x^{2019}$$
= $$(x^{3})^{672} * x^{2}$$ + $$(x^{3})^{673}$$
= $$1^{672} * x^{2}$$ + $$1^{673}$$
= $$x^{2}$$ + 1
= -x
Hence, option C.
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