The value of \sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-......\infty}}} is

Indian Institute of Foreign Trade 2012 Solved Paper

Question : 38 of 128

Marks: +1, -0

The value of

√{7+√{7-√{7+√{7-......∞}}}}

Solution:

Let

√{7+√{7-√{7+√{7-......∞}}}}=x

Thus

√{7+√7-x}=x

⇒7+√{7-x}=x^2

⇒7-x=(x^2-7)^2

Putting options we get,

x=1⇒6≠(-6)^{2}

x=2⇒5≠(-3)^2

x=3⇒4=(9-7)^2

x=4⇒3≠(9)^2

Hence, option C is the correct answer

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