16th Swedish 1976 Problem 2 For which real a are there distinct reals x, y such that x = a - y 2 and y = a - x 2 ?
We have x + y 2 = x 2 + y, so x - y = x 2 - y 2 . Since x ≠ y, we must have x + y = 1. Hence x 2 - x + 1 - a = 0. For distinct real solutions we need 1 > 4(1-a) or a > 3/4. Thanks to Suat Namli 16th Swedish 1976 © John Scholes jscholes@kalva.demon.co.uk 12 February 2004 Last corrected/updated 12 Feb 04