Question 49

If $$x^2 - x - 1 = 0$$, then the value of $$x^3 - 2x + 1$$ is

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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