Correct Answer - Option 1 : 5
Given:
\(√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space \)
Calculation:
Let x be the value of \(√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space \)
Then,
⇒ x = √30 – x
squaring both sides we get,
⇒ x2 = 30 – x
⇒ x2 + x + 30 = 0
⇒ x2 + 6x – 5x + 30 = 0
⇒ x(x + 6) – 5(x + 6) = 0
⇒ (x – 5) (x + 6) = 0
⇒ x = 5 or -6
∴ The required value is 5