Stage: 5 Challenge Level: 
If $x$, $y$ and $z$ are real numbers such that:
$x+y+z=5$
and $xy+yz+zx=3$,
what is the largest value that any one of these numbers can have?
epsilons. Quadratic equations. Simultaneous equations. Pythagoras' theorem. Other equations. Stage 5 - Reviewed 2012. Maximise/minimise/optimise. Long problems. Cubic functions. Graphs.
Published January 1999.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk