Symmetric systems

Vieta’s formulas find their natural application in symmetric systems: systems in which the unknowns $x$ and $y$ appear “interchangeably”, that is, swapping $x$ with $y$ does not change the system. By introducing the sum $S=x+y$ and the product $P=xy$ as new unknowns, these systems are solved elegantly and quickly.

• The sum-product method
• Useful identities with sum and product
• Example of a symmetric system