Skip over navigation
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.
Intersections
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.
You may also like
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?
