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# Algebra Problem

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Let $$x$$ and $$y$$ be real numbers such that  $$xy - \frac{x}{y^2} - \frac{y}{x^2} = 3.$$
Find the sum of all possible values of $$(x-1)(y-1)$$.

Any help would be appreciated!

#1
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The only values that work are x = 2 and y = 2, so (x - 1)(y - 1) = 1.

Dec 1, 2021
#2
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can you tell me how you did this?

#3
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I don't really understand the wording of the question but if it means

$$xy - \frac{x}{y^2} - \frac{y}{x^2} = 3.\\~\\ and\\~\\ (x-1)(y-1)=k$$

Find all possible values of k  then this graph indicates that there are no possible values of k.

https://www.desmos.com/calculator/6bg41jruhs

Dec 2, 2021
#5
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Yes, it does look like it.

Melody  Dec 3, 2021