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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Find the product xy if x and y are rational numbers satisfying the equation:

Perform the multiplication:

and regroup the terms to separate the terms that have an irrational factor:

Since x and y are rational numbers they cannot change the irrational factors. Therefore,

- the irrational term on the left hand side must equal the irrational term on the right hand side
- the rational term on the left hand side must equal the rational term on the right hand side: