The value of expression \sqrt{ 6+\sqrt{6+\sqrt{6+...}} is

SSC CHSL 20 Dec 2015 Shift 1 Paper

Question : 145 of 200

Marks: +1, -0

The value of expression

√{ 6+√{6+√{6+...}}}

Solution:

Let

√{ 6+√{6+√{6+.....}}}=x

..........(1)

√{ 6+(√{6+√{6+.....)}}}=x

.........(2)
Substitute equation (1) in (2)

√{6 + (x) }= x

(or)

x ^2 − x − 6 = 0

x = 3, −2. But 'x' value should be positive
∴ x = 3
Hence, option D is the correct answer.

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