Diaphontine equations

1. Jan 16, 2008

Sam_

So help me with this:

this are simultanious equations.

1/(x^2) + x^2 -7 = 0
&&
1/x + x -y = 0

What is y?

2. Jan 16, 2008

CompuChip

The first one doesn't depend on y, so tackle that one first.
Multiply the first by x^2 and solve it, then plug the result into the second and solve for y.

3. Jan 16, 2008

HallsofIvy

Staff Emeritus
In what sense is this "diophantine equations"? A Diophantine equation is a single equation to be solved in terms of (positive) integers.

4. Jan 16, 2008

dodo

In fact, if these are expected to be solved in integers, there is only one (and plain sight obvious) solution for the second equation.

P.S.: A solution which does not check on the first equation, anyway.
P.P.S.: Oh, sorry, two obvious solutions. I was forgetting there is such thing as negative numbers. Doh! Neither will fit the first equation.

Last edited: Jan 16, 2008
5. Jan 18, 2008

CompuChip

It is plain sight obvious how to solve this system and get the two solutions to it, after which it will be even more plain sight obvious whether they are integers (if not, clearly there are no integer solutions).