MAT 300-02L                         Homework Sheet 4

Spring 2006

 

 

Assignment 10 

 

A.                 Using the Babylonian method of solving systems of equations, find the solution to the following system:

                               xy = 144
                              x+y = 26

B.                 Using the Babylonian method of solving systems of equations, find the solution to the following system:

                               xy = 21
                              x  y =4

C.                 Use our completing the square argument to solve the following problem.  Write the solution in the manner that the Babylonians would have.  You do not need to use sexagesimal numbers; you may use our numbers.

I have added up a square and seven of its sides and get 60.  Find the side of the square.

 

D.                 Use our completing the square argument to solve the following problem.  Write the solution in the manner that the Babylonians would have.  You do not need to use sexagesimal numbers; you may use our numbers.

From the area of my square I have subtracted 12 sides and get 160.  Find the side of the square.

E.                  Verify that lines 10 and 11 of Plimpton 322 are correct.  Note that all you need to do is to show that the given values of d and x produce the correct value of y and .