Algebraic Number/Examples/Golden Mean

Example of Algebraic Number

The golden mean $\phi = \dfrac {1 + \sqrt 5} 2$ is an algebraic number.

Proof

From Golden Mean as Root of Quadratic:

$\phi$ is a root of $x^2 - x - 1 = 0$.

Hence the result by definition of algebraic number.

$\blacksquare$