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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! laugh

 #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
avatar+473 
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can you tell me how you did this?

 #3
avatar+117468 
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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
avatar+117468 
0

Yes, it does look like it. 

Melody  Dec 3, 2021

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