Question

If the infinite series $x=\sqrt{6+\sqrt{6+\sqrt{6+.....}}}$, then the value of $x$ is ;

• A. $2.5$
• B. $3$
• C. $8$
• D. $6$

Answer 1

The correct option is B $3$

Let $x=\sqrt{6+\sqrt{6+\sqrt{\mathrm{6....}}}}$
Squaring both sides, we get

$x^2=6+\sqrt{6+\sqrt{6+.....}}$
$\Rightarrow x^2=6+x$
$\Rightarrow x^2-x-6=0$
$\Rightarrow (x+2)(x-3)=0$
Therefore, $x=3$