1.

if \(y = x + \sqrt {x + \sqrt {x + \sqrt {x + \ldots \infty } } }\), then y(2) =1. 4 or 12. 4 only3. 1 only4. undefined

Answer» Correct Answer - Option 2 : 4 only

\(y = x + \sqrt {x + \sqrt {x + \sqrt {x + \ldots \infty } } } \)

\(\Rightarrow y - x = \sqrt {x + \sqrt {x + \ldots } }\)

\(\Rightarrow y - x = \sqrt y\)

⇒ y = (y –x)2

⇒ y2 + x2 – 2xy – y = 0         

at x = 2, we get,

y2 – 5y + 4 = 0 ⇒ (y - 4) (y - 1) = 0

⇒ y = 4, y = 1

But  At x=2, from the  given equation

 \(y = x + \sqrt {x + \sqrt {x + \sqrt {x + \ldots \infty } } }\),

the value of y will be greater than 2.

So at x=2, y=1 is not possible.



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