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.
The point $X$ moves around inside a rectangle of dimension $p$
units by $q$ units. The distances of $X$ from the vertices of the
rectangle are $a$, $b$, $c$ and $d$ units. What are the least and
the greatest values of
$a^2 + b^2 + c^2 + d^2$
and where is the point $X$ when these values occur?