Evaluate : √(6+(√6+(√6)+..........))

Question

Evaluate : \(\sqrt{6+\sqrt{6+\sqrt{6+....}}}\)

Answer 1

Let y = \(\sqrt{6+\sqrt{6+\sqrt{6+....}}}\)

⇒ y = \(\sqrt{6 + y}\)

⇒ y² = 6 + 7 (On squaring both the sides)

⇒ y² - y - 6 = 0 

⇒ (y - 3)(y + 2) = 0

⇒ y - 3 = 0 or y + 2 = 0

⇒ y = 3 or -2

Neglecting negative value y = 3.