# Babylonian approach to math

1. Mar 27, 2008

### sapiental

1. The problem statement, all variables and given/known data

(1/7)x + (1/11)y = 1 and (6/7)x =(10/11)y

3. The attempt at a solution

I'm doing this problem and we have to do it based on speculated babylonian approach which involves setting x and y equal half the semiperimeter and plus or minus a change in the side of lengths, i/e

x = a/2 + z y = a/2 - z

I'm also trying to really understand this problem area wise, like how it could've been solved involving quadratics.

when I insert the respective formulas

(1/7)(1/2 + z) + 1/11(1/2 - z) = 1

i get x = 35/2 and y = -33/2

this isnt the answer in the book, which is

x = 35/4 and y = 33/4

how can I use the relation of (x - y)^2 = (x +y)^2 - 4xy

does it allow to write (6/7x - 10/11y)^2 = (1/7x + 1/11y)^2 - 4xy?

i know how to find the answer through substitutions but babylonians used the above identy in early multiplication

also, is it possible to construct a "completing the square" diagram in this problem?

thanks!