You may also like

problem icon

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?

problem icon

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?

problem icon

Agile Algebra

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

Fibonacci Fashion

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.