### Real(ly) Numbers

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 of the numbers can have?

### 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.

You might make use of the relationship between the coefficients and the sum and product of the roots of the quadratic equations. Without loss of generality you can take $a \geq b$ and then you'll need to consider separately the case where $a=b$ and where $a> b$.