MathDB

9.2

Part of II Soros Olympiad 1995 - 96 (Russia)

Problems(3)

1/(x+1/(y+1/z)) =7/17 (II Soros Olympiad 1995-96 R1 9.2)

Source:

6/2/2024
Find the integers x,y,zx, y, z for which 1x+1y+1z=717\dfrac{1}{x+\dfrac{1}{y+\dfrac{1}{z}}}=\dfrac{7}{17}
Diophantine equationdiophantinenumber theory
cross out first digit, 1/1996 (II Soros Olympiad 1995-96 R2 9.2)

Source:

6/3/2024
Will the number 1/19961/1996 decrease or increase and by how many times if in the decimal notation of this number the first non-zero digit after the decimal point is crossed out?
algebranumber theory
(1-3a)/(2a + 3) >0, (17 + 4a)/(7 + a) (II Soros Olympiad 1995-96 R3 9.2)

Source:

6/4/2024
The number aa is such that both fractions (1−3a)/(2a+3)   and   (17+4a)/(7+a)(1-3a)/(2a + 3) \,\,\, and \,\,\, (17 + 4a)/(7 + a) are positive. Which one is closer to 5\sqrt5?
algebrainequalities