a) \(P=\dfrac{1}{4\sqrt{x}-4x-2}\)
\(4\sqrt{x}-4x-2=-\left(4x-4\sqrt{x}+1\right)-1=-\left(2\sqrt{x}-1\right)^2-1\le-1\)
\(\Rightarrow P=\dfrac{1}{4\sqrt{x}-4x-2}\ge\dfrac{1}{-1}=-1\)
\(minP=-1\Leftrightarrow x=\dfrac{1}{4}\)
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