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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

15 votes
1 answer
595 views

Solving a non linear equation

I've been trying to prove that the following equation has a unique solution in interval 0 < x < 1 : $$ x = \Big(\frac{1 - (1-x^2)^K}{1 - (1-x)^K}\Big)^2 $$ Where K is a number (integer, if it helps) …