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In this case, rather than working with the awkward numbers, you may find it easier to substitute \alpha = 0.99999 and solve the equations algebraically, and finally substitute 0.99999 for \alpha to find the numerical solutions.
To explain the solutions think about the geometry associated with these equations.
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Age 14 to 18
Challenge Level 
In this case, rather than working with the awkward numbers, you may find it easier to substitute \alpha = 0.99999 and solve the equations algebraically, and finally substitute 0.99999 for \alpha to find the numerical solutions.
To explain the solutions think about the geometry associated with these equations.
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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?
