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?

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.

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

Take a look at the system of equations below:

$ab = 1$

$bc = 2$

$cd = 3$

$de = 4$

$ea = 6$