Solve the system
We set and where . The second equation of course is written as
Now ‘s follow.
Historical note: In the Babylonian signs , tracing back in 1700 BC , there are a lot of geometrical problems that are equivalent to the solution of such systems. In order to be solved the following ( modern ) formulae were used
The above procedure actually led to the discriminant in order for us to solve a second order equation. For example in a book of that age we see the equation . Try to solve this using the above technique.
The above exercise , along with the historical note , can be found at mathematica.gr .