| 1. Transform the equation ab2(1/(a + c)2 + 1/(a - c)2) = (a - b) into a simpler form, given that a > c ≥ 0, b > 0. | |
| 2. Prove or disprove: given any quadrilateral inscribed in a convex polygon, we can find a rhombus inscribed in the polygon with side not less than the shortest side of the quadrilateral. | |
| 3. Let x0 = 5, xn+1 = xn + 1/xn. Prove that 45 < x1000 < 45.1. |
The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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(C) John Scholes
jscholes@kalva.demon.co.uk
19 Apr 2003
Last corrected/updated 19 Apr 2003