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.
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  • 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.
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