### 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.

# Sextet

##### Age 16 to 18 Challenge Level:

If $$x + {1\over x} = 1$$ investigate $$x^n+ {1\over x^n}$$