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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?

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Three by One

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

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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.