Question

Algebra. x * y = 5166, x+y 145. This I know I could do with simply guess and check, but what is the proper algebraic way of doing it? Thanks a lot!

Answer 1

A) x * y = 5,166
B) x + y = 145
y = 5,166/x
x + 5,166/x = 145
x² + 5,166,= 145x
x² -145x + 5,166,= 0
Using quadratic formula to solve:
x = [--145 +-sqroot(21,025 - 4*1*5,166)] / 2*1
x = 145 +-sqroot(21,025 -20,664) / 2
x = 145 +-sqroot(21,025 -20,664) / 2
x = 145 +-sqroot(361) / 2
x = 145 +- 19 / 2

x1 = 164 / 2 = 81

x2= 145 -19 / 2
x2 = 126 / 2
x2 = 63