Ta có: `P` `=` $\dfrac{\sqrt{x}+3}{\sqrt{x}+1}$ `=` $\dfrac{\sqrt{x}+1+2}{\sqrt{x}+1}$ `=` `1` `+` $\dfrac{2}{\sqrt{x}+1}$ với `x` $\geq$ `0`

Xét biểu thức `P` có:
$\sqrt{x}$ $\geq$ `0`

$\sqrt{x}$ `+` `1` `>` `0`

$\dfrac{2}{\sqrt{x}+1}$ `>` `0`

`1` `+` $\dfrac{2}{\sqrt{x}+1}$ `>` `1`

Hay `P` `>` `1`

Suy ra: `P` `>` $\sqrt{P}$ ( vì `P` `>` `1` )

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