Question

If $x + 1 = x^2$ and $x > 0$, then $2x^4$ is:

Accepted Answer

D. $x^2 = x + 1$. $x^4 = (x + 1)^2 = x^2 + 2x + 1 = (x + 1) + 2x + 1 = 3x + 2$. Since $x^2 - x - 1 = 0$ and $x > 0$, $x = \frac{1 + \sqrt{5}}{2}$. $x^4 = 3\left(\frac{1 + \sqrt{5}}{2}\right) + 2 = \frac{7 + 3\sqrt{5}}{2}$. $2x^4 = 7 + 3\sqrt{5}$.

Expression Evaluation from Quadratic Relation

Explanation

Practise this under exam conditions