Can you help me solve this problem?

Question

on a Louvre tablet of about 300 B.C. are four problems concerning rectangles of unit area and given semiperimeter. Let the sides and semiperimeter be x,y, and a. Then we have xy=1, x+y=a. Solve this system by eliminating y and thus obtaining a quadratic in x.

Answer 1

xy = 1

x + y = a → y = a - x

x(a - x) = 1

-x² + ax - 1 = 0

x² - ax + 1 = 0