\(1,x-\sqrt{x}=x-\sqrt{x}+\dfrac{1}{4}-\dfrac{1}{4}=\left(\sqrt{x}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
Dấu \("="\Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\)
\(2,-x+10\sqrt{x}-27=-\left(x-10\sqrt{x}+25\right)-2=-\left(\sqrt{x}-5\right)^2-2\le-2\)
Dấu \("="\Leftrightarrow\sqrt{x}=5\Leftrightarrow x=25\)
\(3,\dfrac{\sqrt{x}+7}{\sqrt{x}+1}=1+\dfrac{6}{\sqrt{x}+1}\\ \sqrt{x}+1\ge1\Leftrightarrow\dfrac{6}{\sqrt{x}+1}\ge\dfrac{1}{6}\Leftrightarrow1+\dfrac{6}{\sqrt{x}+1}\ge\dfrac{7}{6}\)
Dấu \("="\Leftrightarrow x=0\)
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