Cho 3 số x,y,z thỏa mãn $x > y > z > 0$. CMR:
$\frac{y}{\sqrt{x + y} - \sqrt{x - y}} < \frac{z}{\sqrt{x + z} - \sqrt{x - z}}$
Cho 3 số x,y,z thỏa mãn $x > y > z > 0$. CMR:
$\frac{y}{\sqrt{x + y} - \sqrt{x - y}} < \frac{z}{\sqrt{x + z} - \sqrt{x - z}}$
"I am the bone of my sword,
Unknown to Death, Nor known to Life,
So as I pray, unlimited blade works."
Cho 3 số x,y,z thỏa mãn $x > y > z > 0$. CMR:
$\frac{y}{\sqrt{x + y} - \sqrt{x - y}} < \frac{z}{\sqrt{x + z} - \sqrt{x - z}}$
$\frac{y}{\sqrt{x + y} - \sqrt{x - y}} < \frac{z}{\sqrt{x + z} - \sqrt{x - z}}$
$\Leftrightarrow$$\frac{\sqrt{x+y}+\sqrt{x-y}}{2}<\frac{\sqrt{x+z}+\sqrt{x-z}}{2}$
$\Leftrightarrow$$2x+2\sqrt{x^{2}-y^{2}}<2x+2\sqrt{x^{2}-y^{2}}$
$\Leftrightarrow$$x^{2}-y^{2}<x^{2}-z^{2}$$\Leftrightarrow$y>z (đúng)
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