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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.
Quadratic Harmony
Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
Age 16 to 18 Challenge Level:
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 one of these numbers can have?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.