Lời giải

Chọn A

Do $\left\{ {\begin{array}{*{20}{c}}{MN\;{\rm{//}}\;BC}\\{\left( \alpha \right) \cap \left( {SBC} \right) = PQ}\end{array}} \right.$ $\Rightarrow PQ\;{\rm{//}}\;BC$.

$\frac{{{V_{S.MNQ}}}}{V} + \frac{{{V_{S.NPQ}}}}{V} = \frac{{{V_1}}}{V}$ $\Leftrightarrow$$\frac{{{V_{S.MNQ}}}}{{2{V_{S.ABD}}}} + \frac{{{V_{S.NPQ}}}}{{2{V_{S.BCS}}}} = \frac{1}{2}$ $\Leftrightarrow \frac{{SM}}{{SA}}.\frac{{SN}}{{SD}}.\frac{{SQ}}{{SB}} + \frac{{SP}}{{SC}}.\frac{{SN}}{{SD}}.\frac{{SQ}}{{SB}} = 1$ $\Leftrightarrow \frac{x}{4} + \frac{{{x^2}}}{2} = 1$ $\Leftrightarrow 2{x^2} + x - 4 = 0$ $\Leftrightarrow x = \frac{{ - 1 + \sqrt {33} }}{4}$ (vì $x > 0$).