Question

The value(s) of $x$ satisfying the equation $x=\sqrt{20+\sqrt{20+\sqrt{20+\cdots }}}$ is

• A. both $-4$ and $5$
• B. $0$
• C. $-4$
• D. $5$

Answer 1

The correct option is D $5$

$x=\sqrt{20+\sqrt{20+\sqrt{20+\cdots }}}$
$\Rightarrow x=\sqrt{20+x}$
$\Rightarrow x^2-x-20=0$
$\Rightarrow x=-4,5$
Since, $x$ can't be negative,
$\therefore x=5$