### Janusz Asked

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

### 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?

### Agile Algebra

Observe symmetries and engage the power of substitution to solve complicated equations.

# Fibonacci Fashion

##### Stage: 5 Challenge Level:

Parts (2) and (3) of this problem use the results of previous parts.

In part (4) try some small values of $n$, look for a pattern and make a conjecture about the result you suspect might always be true, then prove your conjecture.