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1991 AIME Question 7

AIME · 1991 AIME

Question 7

Find $A^2,$ where $A$ is the sum of the absolute values of all roots of the following equation: $$
x=\sqrt{19}+\cfrac{91}{\sqrt{19}+\cfrac{91}{\sqrt{19}+\cfrac{91}{\sqrt{19}+\cfrac{91}{\sqrt{19}+\cfrac{91}{x}}}}}.
$$