19th Swedish 1979 Problem 2 Find rational x in (3, 4) such that √(x-3) and √(x+1) are rational.
eg 3 49/144 Solution Put x = 3 + a2, then we need a2 + 4 = b2 with a and b rational. Put c = b-a, then b+a = 4/c, so a = (4/c - c)/2. We need 0 < a < 1. Try c = 3/2, then a = 7/12 and x = 3 49/144 and it is easy to check that this works. Thanks to Suat Namli 19th Swedish 1979 © John Scholes jscholes@kalva.demon.co.uk 13 February 2004 Last corrected/updated 13 Feb 04