IIFT 2012 Question Paper

Question 38

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

Solution

Let, $$\sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-.....\infty}}}}$$ = $$x$$
Thus, $$\sqrt{7+\sqrt{7-x}}$$ = $$x$$
=> $$7+\sqrt{7-x} = x^2$$
=> $$7-x = (x^2-7)^2$$
Putting options we get,
x=1 => 6$$\neq(-6)^2$$
x=2 => 5$$\neq(-3)^2$$
x=3 => 4=$$(9-7)^2$$
x=4 => 3$$\neq(9)^2$$
Hence, option C is the correct answer.


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