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You have the "repeated fraction" x= 2+ 1/(2+ 1/(2+ 1/...)) Notice that is x= 2+ 1/A where A= 2+ 1/(2+ 1/...) which is just "x" again. Your equation is the same as x= 2+ 1/x. Multiply both sides by x to get a quadratic equation and solve for x.
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