Expert: Sherman D. - 7/24/2004

Question
this is the problem
"Find two positive itegers whose sum is 12 and the sum of whose recprocals is 3/8."

Using trial and errror I found the only only possible solution to be 4 and 8 b/c 4+8=12 and 1/4+1/8=3/8 but the problem is that my teacher insist that we use the Gaussian-Jordan method to solve the problem but
when i do that I get no solution.
ex.
|1 1 ] 12| (row 1)
|1 1 ] 8/3| (row 2)

|1 1 ] 12|
|0 0 ] 28/3| (new row2) = (row1) - (row2)

what am I doing wrong?

Any help is greatly apreciated, thank you.
alex

Answer
x + y = 12
(1/x) + (1/y) = (3/8)

x + y = 12
y = -x + 12

(1/x) + (1/(-x + 12)) = (3/8)

(1/x) + (1/(-(x - 12))) = (3/8)

(1/x) - (1/(x - 12)) = (3/8)

Multiply everything by 8x(x - 12)

8(x - 12) - 8x = 3(x(x - 12))

8x - 96 - 8x = 3(x^2 - 12x)

-96 = 3x^2 - 36x

3x^2 - 36x + 96 = 0

x^2 - 12x + 32 = 0

(x - 4)(x - 8) = 0

x = 4 or 8

so the answer is 4 and 8.

that is what i did.

Since i don't know the Gaussian-Jordan method, maybe you can see what i did, and maybe you can use that to do the method for yourself.