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 of the numbers can
Find all the solutions to the this equation.
Four vehicles travelled on a road with constant velocities. The car
overtook the scooter at 12 o'clock, then met the bike at 14.00 and
the motorcycle at 16.00. The motorcycle met the scooter at 17.00
then it overtook the bike at 18.00. At what time did the bike and
the scooter meet?
This is another inverse problem. If you were given the equations and asked to draw the graphs then graphing software would do the work for you. This challenge is posed the opposite way round. You have to use mathematical reasoning to deduce the equations of the graphs in the illustration. Then you can use graphing software to check to see if your reasoning was correct.
You can read about one teacher's experience of using this task in the classroom.