### 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?

### Pair Squares

The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.

### Escriptions

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

# Real(ly) Numbers

##### Stage: 5 Challenge Level:

If $x$, $y$ and $z$ are real numbers such that:

$x+y+z=5$

and $xy+yz+zx=3$,

what is the largest value that any one of these numbers can have?