3 replies to this topic

[robot3d]

cho a,b,c là các số thực dương tùy ý. CMR:

$\frac{ab}{c}+\frac{bc}{a}+\frac{ac}{b}\geq \sqrt{3(a^2+b^2+c^2)}$

[phamngochung9a]

cho a,b,c là các số thực dương tùy ý. CMR:

$\frac{ab}{c}+\frac{bc}{a}+\frac{ac}{b}\geq \sqrt{3(a^2+b^2+c^2)}$

$\left ( \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} \right )^{2}\geq 3.\left ( \sum \frac{ab}{c}.\frac{bc}{a} \right )=3\left ( a^{2}+b^{2}+c^{2} \right )\Rightarrow \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\geq \sqrt{3\left ( a^{2}+b^{2}+c^{2} \right )}$

[Kira Tatsuya]

đúng rồi :3 

Edited by Kira Tatsuya, 23-11-2015 - 21:45.

[robot3d]

$\left ( \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} \right )^{2}\geq 3.\left ( \sum \frac{ab}{c}.\frac{bc}{a} \right )=3\left ( a^{2}+b^{2}+c^{2} \right )\Rightarrow \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\geq \sqrt{3\left ( a^{2}+b^{2}+c^{2} \right )}$

tks. t sd sai dt phụ nên k ra.