3

Part of 1978 Canada National Olympiad

Problems(1)

Find largest z from system

Source: Canadian Mathematical Olympiad - 1978 - Problem 3.

Determine the largest real number

z

such that \begin{align*} x + y + z = 5 \\ xy + yz + xz = 3 \end{align*} and

x

y

inequalities unsolvedinequalities