Interesting article! I think there's an error though, where the first constraint should be expressed as "(5-x) + (x-5) = 10" (the author has "(x-5) + (x-5) = 10" currently).
5+x and 5-x, you mean. they did get that right when substituting in the cubic equation.
fixed that, thanks a lot for the correction.
> Pierre de Fermat was a famous 16th-century French mathematician...