Question

The value of $\sqrt{8+2\sqrt{8+2\sqrt{8+2\sqrt{8+...\infty }}}}$ is

• A. $6$
• B. $-2$ and $4$
• C. $4$
• D. $8$

Answer 1

The correct option is C $4$

Let $x=\sqrt{8+2\sqrt{8+2\sqrt{8+2\sqrt{8+...\infty }}}}$
$\Rightarrow x=\sqrt{8+2x}$
$\Rightarrow x^2-2x-8=0$
$\Rightarrow (x-4)(x+2)=0$
$\Rightarrow x=4(\because x>0)$