MathDB

1/x+4/y+9/z=3, x+y+z<=12, x,y,z >0

Source: JBMO 2008 Shortlist A5

October 14, 2017

JBMOalgebrasystem of equations

Problem Statement

Find all triples

(x, y, z)

of real positive numbers, which satisfy the system

\begin{cases} \frac{1}{x}+\frac{4}{y}+\frac{9}{z}=3 \\ x + y + z \le 12 \end{cases}