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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.

Impedance Can Be Complex!

Age 16 to 18 Challenge Level:

This problem makes use of the concepts of AC generators and RMS (root-mean-square) voltage.You will also need to be familiar with complex numbers in order to attempt this problem.

You may wish to read our articles on AC/DC circuits for the background physics and mathematics required.