// minds behind maths
Diophantus
c. 200–284 CE · Algebra, number theory
Diophantus of Alexandria was a Greek mathematician often called one of the fathers of algebra. His work Arithmetica, a collection of problems solved with equations, introduced an early symbolic notation for an unknown and its powers, and is filled with the kind of identity manipulation and substitution used to expand and factor algebraic expressions. Equations requiring whole-number solutions are still called Diophantine equations in his honour, and Arithmetica directly influenced later algebraists including Viète and Fermat.
Source: Wikipedia — Diophantus
Formulas that trace back to Diophantus
If x + 1/x = a, then x² + 1/x² = a² − 2
x + 1/x = a => x² + 1/x² = a² - 2
If x + 1/x = a, then x³ + 1/x³ = a³ − 3a
x + 1/x = a => x³ + 1/x³ = a³ - 3a
If x − 1/x = a, then x² + 1/x² = a² + 2
x - 1/x = a => x² + 1/x² = a² + 2
If x − 1/x = a, then x³ − 1/x³ = a³ + 3a
x - 1/x = a => x³ - 1/x³ = a³ + 3a