Question

The value of `sqrt(6 + sqrt(6 + sqrt(6 ....)))`

पर्याय

• 3.5

• 4

• 3

• –3

Answer 1

3

Explanation:

Let `sqrt(6 + sqrt(6 + sqrt(6 ....)))` = y

⇒ `sqrt(6 + "y")` = y

6 + y = y²

⇒ y² − y − 6 = 0

⇒ y² − (3 − 2)y − 6 = 0

⇒ y² − 3y + 2y − 6 = 0

⇒ y(y − 3) + 2(y − 3) = 0

⇒ (y − 3) (y + 2) = 0

⇒ y = 3, −2

Since y cannot be negative as negative square root is not real so y = 3.