MathDB

2

Part of 2001 Federal Competition For Advanced Students, Part 2

Problems(2)

Solve the system: x+y+z=6, 1/x+1/y+1/z=2-4/(xyz)

Source: Austrian Mathematical Olympiad 2001, Part 2, D1, P2

6/25/2011
Determine all triples of positive real numbers (x,y,z)(x, y, z) such that x+y+z=6,x+y+z=6,1x+1y+1z=2−4xyz.\frac 1x + \frac 1y + \frac 1z = 2 - \frac{4}{xyz}.
algebra proposedalgebra
All integers m that roots of 3x^3-3x^2+m = 0 are rational

Source: Austrian Mathematical Olympiad 2001, Part 2, D2, P2

6/25/2011
Determine all integers mm for which all solutions of the equation 3x3−3x2+m=03x^3-3x^2+m = 0 are rational.
quadraticsnumber theory proposednumber theorypco