Solution
$$x^2 - x - 1 = 0$$
$$x^2 = 1 + x$$ Or $$x^2 - x = 1$$
$$= x^3 - 2x + 1 = x.x^2 - 2x + 1$$
$$=x.(1 + x) - 2x + 1$$
$$=x + x^2 - 2x + 1$$
$$=x^2 - x + 1$$
$$=1 + 1$$
= 2
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$$x^2 - x - 1 = 0$$
$$x^2 = 1 + x$$ Or $$x^2 - x = 1$$
$$= x^3 - 2x + 1 = x.x^2 - 2x + 1$$
$$=x.(1 + x) - 2x + 1$$
$$=x + x^2 - 2x + 1$$
$$=x^2 - x + 1$$
$$=1 + 1$$
= 2
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