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Sequence of functions

Source: Problem 4, Polish NO 1992

October 1, 2005
functioninductioninequalitiesalgebra unsolvedalgebra

Problem Statement

The functions f0,f1,f2,...f_0, f_1, f_2, ... are defined on the reals by f0(x)=8f_0(x) = 8 for all xx, fn+1(x)=x2+6fn(x)f_{n+1}(x) = \sqrt{x^2 + 6f_n(x)}. For all nn solve the equation fn(x)=2xf_n(x) = 2x.
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