Question

Evaluate
$\sqrt{6 + \sqrt{6 + \sqrt{6} ......} }$
​

Answer 1

$\huge{\bold{SOLUTION:-}}$

$y = \sqrt{6 + \sqrt{6 + \sqrt{6} .....} }$

$= y = \sqrt{6 + y}$

${y}^{2} - y - 6 = 0$

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

$y = 3$

"Negative value is neglected here"

While doing this type of problems ,

First assume the whole value by using the variables like x or y

Now , compress the problem into a simpler one

After factorise the problem

you will get the value of x or y or any variable what you have taken.