An infinite fraction with square roots

Algebra Level 3

Evaluate A 2 A^2 where A A is the sum of the absolute value of all roots of the following equation:

x = 19 + 91 19 + 91 19 + 91 19 + 91 19 + 91 x x = \sqrt{19} + \dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{{\sqrt{19}+\dfrac{91}{x}}}}}}}}}


The answer is 383.

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