Question

The value of the expression $\sqrt{6+\sqrt{6+\sqrt{6+\cdots +\infty }}}$ is

• A. 2
• B. 3
• C. 30
• D. 5

Answer 1

Answer: (B)

3

Let $y=\sqrt{6+y}$
On squaring both sides, we get
$y^2=6+y$
$y^2-y-6=0$
$y^2-3y+2y-6=0$
$(y-3)(y+2)=0$
$y=3,-2$
But $y$ can not be negative.
Hence, $y=3$ is the answer.