if y=√(6+√(6+√(6+......∞,find y
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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
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
Anonymous:
hope it helps
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