You may also like

Kissing

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

Target Six

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

Power Quady

Age 16 to 18
Challenge Level


Find all real solutions of the equation
$$(x^2-7x+11)^{(x^2-11x+30)} = 1.$$


You may also be interested in the problem Mega Quadratic Equations.
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 - 2021. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.