Question

answer me plz with all step​

Answer 1

Solution :

Let, x = $\sqrt{20+\sqrt{20+\sqrt{20+...}}}$

Squaring both sides, we get

$x^{2}=20+\sqrt{20+\sqrt{20+\sqrt{20+...}}}$

  ⇒ x² = 20 + x

  ⇒ x² - x - 20 = 0

  ⇒ x² - 5x + 4x - 20 = 0

  ⇒ x (x - 5) + 4 (x - 5) = 0

  ⇒ (x - 5) (x + 4) = 0

Either x - 5 = 0 or, x + 4 = 0

⇒ x = 5 , - 4

Here, x is obviously > 0

Thus, x = 5

⇒ $\sqrt{20+\sqrt{20+\sqrt{20+...}}}$ = 5