Critical points with multiple variables

HAL10000
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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.
 
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HAL10000 said:

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