[Toán 9] So sánh căn thức

N

noinhobinhyen

Giả sử :

$\sqrt[]{2005}-\sqrt[]{2004} \geq \sqrt[]{2004}-\sqrt[]{2003}$

$\Leftrightarrow \sqrt[]{2005}+\sqrt[]{2003} \geq 2\sqrt[]{2004}$

$\Leftrightarrow (\sqrt[]{2005}+\sqrt[]{2003})^2 \geq (2\sqrt[]{2004})^2$

$\Leftrightarrow 4008 + 2\sqrt[]{2005.2003} \geq 4008+4008$

$\Leftrightarrow 2\sqrt[]{2005.2003} \geq 4008$

$\Leftrightarrow \sqrt[]{2005.2003} \geq 2004$

$\Leftrightarrow \sqrt[]{(2004+1)(2004-1)} \geq 2004$

$\Leftrightarrow \sqrt[]{2004^2-1} \geq \sqrt[]{2004^2}$

Vô lí . Vậy ...
 
L

luffy_1998

Câu so sánh:
$\sqrt{2005} - \sqrt{2004} = \dfrac{1}{\sqrt{2005} + \sqrt{2004}} < \dfrac{1}{\sqrt{2004} + \sqrt{2003}} = \sqrt{2004} - \sqrt{2003}$.
 
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