Find out the value of \sqrt {6+ \sqrt{6 + \sqrt{6 +\sqrt 6}.}... = ?

SSC CPO SI and ASI Model Paper 5

Question : 112 of 200

Marks: +1, -0

Find out the value of

√ {6+ √{6 + √{6 +√ 6}}.}... = ?

Solution:

Let

{√{6 +√{6 + √{6 +√6}}}}.... = x

⇒√{6 +x }=x

By squaring both sides,

⇒ x^2 = 6 + x

⇒ x^2 – x – 6 = 0

⇒ (x+2)(x – 3) = 0

⇒x = 3, x = –2 is not possible.Therefore, the value of x will be 3.

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