Alan

The quadratic 2x^2 - 3x + 11 = 0  has two imaginary roots. What is the sum of the squares of these roots?

As follows:

NB It is worth committing 30-60-90 and 45-45-90 triangles to memory.

f(3) = g(g(3)) - g(3)

g(3) = 2*3 - 7 = -1

g(g(3)) = g(-1) = -2 - 7 = -9

f(3) = -9 - (-1) = -8

Alternatively, you could use the closed form expression for Lucas numbers:

Apologies, I've misled you by reacting too quickly, with too little thought!  

With dot products  u•v = |u|*|v|*cos(theta), where |u| is the magnitude of u, and theta is the angle between u and v. This means that

v•u = |v|*|u|*cos(theta) = u•v 

The same is true for the other dot products.

(u + 2v)•w = u•w + 2*v•w = 4 + 2*5 = 14

Look at the graph and see if you can decide from that:

Here are graphs of the individual functions:

This question keeps cropping up!!

What about one 1 and one 6?