You may also like

Roots and Coefficients

If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?

Three by One

There are many different methods to solve this geometrical problem - how many can you find?

Target Six

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

Thousand Words

Age 16 to 18 Challenge Level:

Care needs to be taken over values of $\alpha$ and $\beta$ greater than $2\pi$.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Copyright © 1997 - 2020. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.