Question

if y=√(6+√(6+√(6+......∞,find y

Answer 1

y = √(6+√(6+√(6+......∞
y² = 6+√(6+√(6+......∞
⇒ y² - 6 = √(6+√(6+√(6+......∞ 
⇒ y² - 6 = y             {as y = √(6+√(6+√(6+......∞ }
⇒ y² - y - 6 = 0
⇒ y² - 3y + 2y - 6 = 0
⇒y(y - 3) + 2(y - 3) = 0
⇒ (y - 3)(y + 2) = 0

y = 3 or - 2

neglecting the negative value we have y = √(6+√(6+√(6+......∞ = 3