Question

find the equation if x=root5+root5+root5.............infinity

Answer 1

see the picture for the solution

Answer 2

Answer:

$x^{2} -x-5=0$

Step-by-step explanation:

Here, the given equation is

$x = \sqrt{5+\sqrt{5+\sqrt{5.........infinity} } } ............................(1)$

and we find the equation from this given equation

In the given equation we can take

$x=\sqrt{5+\sqrt{5........infinity} }$

putting the value of x in Equation (1) , we get

$x= \sqrt{5+x}$

taking a square of both sides, we get

$x^{2} = (\sqrt{5+x} )^{2} \\\\x^{2} = 5 +x\\\\x^{2} -x-5=0$

It is the resultant equation.