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?

Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

System Speak

Stage: 4 and 5 Challenge Level:

Solve the system of equations:

$ab = 1$

$bc = 2$

$cd = 3$

$de = 4$

$ea = 6$