Puzzles
Split 10 into two parts where one part squared is four times their product
Divide the number ten into two parts. Multiply the two parts together, and separately multiply one of the parts by itself. It turns out the self-multiplied result is exactly four times the product of the two parts. What are the two parts?
Reveal the answer
The parts are 8 and 2: 8 squared is 64, and 4 times (8 times 2) is also 64. This is one of the worked 'divide ten into two parts' example problems al-Khwarizmi used to demonstrate solving quadratic equations by 'completion and balancing' (al-jabr wal-muqabala), the book that gave algebra its name.