Critical points with multiple variables

[HAL10000]

Homework Statement

Locate and classify the critical points of f(x,y) = (x-y)(xy-1).

Homework Equations

The Attempt at a Solution

I found the partial derivatives with respect to x and y and I got:

∂f/∂x = -y²+2xy-1 ∂f/∂y = x²-2xy+1

After setting them both equal to zero I can't find a way to solve for x and y.

 

[Mark44]

Homework Statement

Locate and classify the critical points of f(x,y) = (x-y)(xy-1).

Homework Equations

The Attempt at a Solution

I found the partial derivatives with respect to x and y and I got:

∂f/∂x = -y²+2xy-1 ∂f/∂y = x²-2xy+1

After setting them both equal to zero I can't find a way to solve for x and y.

So your equations are y² - 2xy +1 = 0 and x² - 2xy + 1 = 0.

Or y² = 2xy -1, and x² = 2xy - 1.

Can you continue from here?

 

[HAL10000]

wow, yes, thank you this is what happens when you do too many of these problems in one night