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![\[ \frac{\displaystyle\sum_{k=0}^r \binom nk \binom{n-2k}{r-k}}{\displaystyle\sum_{k=r}^n \binom nk \binom{2k}{2r}\left(\frac{3}{4}\right)^{n-k}\left(\frac{1}{2}\right)^{2k-2r}}\]](http://latex.artofproblemsolving.com/9/d/e/9dedd490eaf9c6d22aaf93bbd74d82375adcfa85.png)
where

Options: 1/2, 1, 2, none.
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\[ \left((x^2+1)+(\sqrt{2}x+\sqrt{2})\right)\left((x^2+1)-(\sqrt{2}x+\sqrt2})\right)= 0 \]
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