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
Four rods are hinged at their ends to form a quadrilateral with
fixed side lengths. Show that the quadrilateral has a maximum area
when it is cyclic.
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the
parameter t varies.
Given that $u> 0$ and $v> 0$ what is the smallest possible
value of $1/u + 1/v$ given that $u + v = 5$?
Can you find this value by more than one method (not involving
trial and error) without using calculus?