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Babylonian approach to math

  1. Mar 27, 2008 #1
    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?

  2. jcsd
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