Question

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Answer 1

Lời giải:
\(B=\frac{2x+\sqrt{x}-4}{(\sqrt{x}+1)(\sqrt{x}-2)}-\frac{(\sqrt{x}+2)(\sqrt{x}-2)}{(\sqrt{x}+1)(\sqrt{x}-2)}+\frac{\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}\)

\(=\frac{2x+\sqrt{x}-4-(x-4)+\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}=\frac{x+2\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}=\frac{(\sqrt{x}+1)^2}{(\sqrt{x}+1)(\sqrt{x}-2)}=\frac{\sqrt{x}+1}{\sqrt{x}-2}\)

\(P=AB=\frac{3\sqrt{x}-4}{\sqrt{x}+1}.\frac{\sqrt{x}+1}{\sqrt{x}-2}=\frac{3\sqrt{x}-4}{\sqrt{x}-2}\)

\(P\geq 2\Leftrightarrow \frac{3\sqrt{x}-4}{\sqrt{x}-2}\geq 2\)

\(\Leftrightarrow \frac{3\sqrt{x}-4}{\sqrt{x}-2}-2\geq 0\Leftrightarrow \frac{\sqrt{x}}{\sqrt{x}-2}\geq 0\)

\(\Leftrightarrow \sqrt{x}-2>0\Leftrightarrow x>4\)

Kết hợp với ĐKXĐ suy ra $x>4$