Algebra Problem

Question

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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!

Guest · Answer 1 · 2021-12-01T11:07:43

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

Melody · Answer 2 · 2021-12-02T07:27:33

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.