Question

$\sqrt{20 + \sqrt{20 + \sqrt{20 \times .. \infty } } }$
​

Answer 1

Answer:

5

Step-by-step explanation:

Let the value of this infinitely nested root sum be x(or whatever you want to call it)

⇒x =  $\sqrt{20 + \sqrt{20 + \sqrt{20 + \sqrt{20 + ...} } } }$  ----------(1)

⇒x = $\sqrt{20 + x}$

⇒ x² = 20 + x [squaring both sides]

⇒x² - x - 20 = 0

⇒x² -5x + 4x - 20 = 0

⇒x( x - 5 ) + 4( x - 5 ) = 0

⇒( x - 5 )( x + 4 ) = 0

⇒ x = 5 , x = -4

∵ From the question, we can see that only the positive root is taken into consideration,

∴ x ≠ 4

⇒ x = 5

Therefore the value of the above infinitely nested root sum is 5