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Really hard problem!!

$$ \begin{align} xy&=-2 \\ xy^{a-1} &=-512 \\ x(y^a-1 ) &= 341y-341 \end{align} $$

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    Plugging the 1st and 2nd equations into the 3rd, we get a quadratic equation for y.2011-11-09
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    Did you want the third equation to be $x(y^a-1)=-341y-341$? The solution is much nicer then.2011-11-09

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