# Math Help - Quadratic question

1. ## Quadratic question

Please refer to the attached question.

2. Originally Posted by yeoky
Find the value of $1 + \frac{3}{1 + \frac{3}{1 + \frac{3}{1 + ... }}}$

Let the value be x. Then you have to solve $x = 1 + \frac{3}{x}$.

3. Hello, yeoky!

$\text{Find the value of: }\;x \;=\;1 + \frac{3}{1 + \dfrac{3}{1 + \dfrac{3}{1 + \hdots}}}$

$\text{We have: }\;x \;=\;1 + \frac{3}{\begin{Bmatrix}1 + \dfrac{3}{1 + \dfrac{3}{1 + \hdots}}\end{Bmatrix}} \;\;\begin{array}{c}\\ \\ \\ \leftarrow\:\text{ This is }x \end{array}$

That is: . $x \;=\;1 + \frac{3}{x}$

Multiply by $x\!:\;\;x^2 \:=\:x + 3 \quad\Rightarrow\quad x^2 - x - 3 \:=\:0$

Quadratic Formula . $x \;=\;\frac{1 \pm\sqrt{13}}{2}$

Since $x$ is positive: . $x \;=\;\frac{1 + \sqrt{13}}{2}$