ứng dụng BĐT cauchy

L

linhhuyenvuong

$ S^2 = \frac{a^2b^2}{c^2}+\frac{b^2c^2}{a^2}+\frac{c^2a^2}{b^2}+2(a^2+b^2+c^2 )= \frac{a^2b^2}{c^2}+\frac{b^2c^2}{a^2}+\frac{c^2a^2}{b^2}+2 $

[TEX] \frac{a^2b^2}{c^2}+\frac{b^2c^2}{a^2} \geq 2b^2[/TEX]
tt
[TEX] \Rightarrow \frac{a^2b^2}{c^2}+\frac{b^2c^2}{a^2}+\frac{c^2a^2}{b^2}\geq a^2+b^2+c^2=1 [/TEX]
[TEX]\Rightarrow S^2 \geq3\Rightarrow S \geq\sqrt{3}[/TEX]

'[TEX]'='' \Leftrightarrow a=b=c=\frac{1}{\sqrt{3}} [/TEX]
 
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