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USAMO 1990 Problem 2

  • Day 1
  • Answer

Define f1(x)=(x2+48)f_{1}(x)=\sqrt{ }\left(x^{2}+48\right) and fn(x)=(x2+6fn−1(x))f_{n}(x)=\sqrt{ }\left(x^{2}+6 f_{n-1}(x)\right). Find all real solutions to fn(x)=2xf_{n}(x)=2 x.

Dataset text NuminaMath olympiads. Quoted with source.

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x=4

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