The value of the expression √(6+√(6+√(6+…..+ ))) up to ∞ is :

  1. 3
  2. 2
  3. 30
  4. 5
Anurag Mishra Professor Asked on 29th December 2015 in Maths.
Add Comment
1 Answer(s)

Answer: (1) 3         

Explanation:-
√(6+√(6+√(6+…..+ )))

Let X = √(6+√(6+…..+ ))
Then, X = √(6+ X)
Square root on both side,
X² = 6 + X
X² – X – 6 = 0
X² – 3 X + 2 X – 6 = 0
X (X – 3) + 2 (X – 3) = 0
(X + 2) (X – 3) = 0
X = 3, – 2

But – 2 < 0  therefore, X = 3.

Then, the value of √(6+√(6+√(6+…..+ ))) is 3.

Hence, the correct answer is option (1) 3.

Monis Rasool Professor Answered on 29th December 2015.
Add Comment

Your Answer

By posting your answer, you agree to the privacy policy and terms of service.