Question

if root x+root x+root x+ infniety =6 then find the value of x

Answer 1

Please see the attachment

Answer 2

The vaue of "x is equal to 30".

Step-by-step explanation:

We have,

$\sqrt{x+\sqrt{x}+\sqrt{x}+\sqrt{x}+....}=6$     ......(1)

To find, the value of x=

Let $y=\sqrt{x+\sqrt{x}+\sqrt{x}+\sqrt{x}+....}$

Put $y=\sqrt{x+\sqrt{x}+\sqrt{x}+\sqrt{x}+....}$ in (1), we get

$\sqrt{x+y}=6$                                         ......(2)

Squaring (1), we get

$(\sqrt{x+y})^{2} =6^{2}$

⇒ $x+y =36$

⇒ $x=36-y$

⇒ $x=30$

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

Hence, the vaue of "x is equal to 30".