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An infinite nested radical

EasyBrainteasers~3m

Evaluate 6+6+6+⋯\sqrt{6 + \sqrt{6 + \sqrt{6 + \cdots}}} (the infinitely nested radical).

Show hints (2)+
  1. Set x=6+xx=\sqrt{6+x} (the inner tail equals the whole).
  2. Solve x2−x−6=0x^2-x-6=0 and take the non-negative root.

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Asked at: Jane Street, Optiver

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