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| Math Central | Quandaries & Queries |
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Question from Anagh: If x and y are rational numbers and Then find the value of x and y. |
Hi,
Let's rewrite this as
\[(x + y) - (2x - y) = (x - y - 1)\sqrt{5} - (x-2y) \sqrt{2}.\]
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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