



 
Hi, Let's rewrite this as \[(x + y)  (2x  y) = (x  y  1)\sqrt{5}  (x2y) \sqrt{2}.\] If $x$ and $y$ are rational then the left side of the above equation is rational and so are $x  y  1$ and $x  2y.$ But if $a$ and $b$ are rational then \[a\sqrt{5} + b \sqrt{2}\] is rational only if $a = b = 0.$ Penny  


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