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\sqrt{2}

Source: Canada 1972, Problem 7

June 25, 2006
quadraticslimitalgebrabinomial theorem

Problem Statement

a) Prove that the values of xx for which x=(x2+1)/198x=(x^2+1)/198 lie between 1/1981/198 and 197.99494949⋯197.99494949\cdots. b) Use the result of problem a) to prove that 2<1.41421356‾\sqrt{2}<1.41\overline{421356}. c) Is it true that 2<1.41421356\sqrt{2}<1.41421356?
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