### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

### 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?

### Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

# Proof Sorter - Quadratic Equation

##### Stage: 4 and 5 Challenge Level:

Which blue statement looks like a starter?

Which line of algebra looks like it belongs with that statement?

Now look at the actions on offer : Subtract, Divide, Take and Complete. Can you find a line of algebra to go with each of those?

Is there a sequence you can find by following the algebra?

Remember, the scale at the side tells you how you are doing.