200 Followers problem

Algebra Level 3

Which of these numbers have a larger value?

1)

\[ \sqrt{200 -17 \sqrt{ 200 -17 \sqrt {200 -17 \sqrt{ 200 -17 \ldots}}}} \]

2)

\[ \sqrt{200 \sqrt{ 200 \sqrt {200 \sqrt{ 200 \ldots}}}} \]

Let \(a\) be the value of the first nested radical, and \(b\) be the values of the second nested radical.

If \(a\) is greater provide the answer as, \((a+b)^{2}\), if \(b\) is greater provide the answer as \((a-b)^{2}\).

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