Question

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

• A. 2
• B. 3
• C. 30
• D. 5

Answer 1

The correct option is B 3

Consider the given expression,

Let,

$x=\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{\mathrm{6..........}\infty }}}}$

Now,

$x=\sqrt{6+x}$

$x^2=6+x$

$x^2-x-6=0$

$x^2-3x+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x-3)(x+2)=0$

$x=3or-2$

Hence,this is the answer.