5 replies to this topic

[Sin99]

Cho a,b,c >1 thõa mãn : $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} =2$

CMR: $\sqrt{a-1}+\sqrt{b-1}+\sqrt{c-1}\leq \sqrt{a+b+c}$ 

[DOTOANNANG]

$$\sqrt{a+ b+ c}= \sqrt{\left ( a+ b+ c \right )\left ( \frac{a- 1}{a}+ \frac{b- 1}{b}+ \frac{c- 1}{c} \right )}\geqq \sqrt{a- 1}+ \sqrt{b- 1}+ \sqrt{c- 1}$$

 

$\lceil$ Bất đẳng thức Holder! $\rfloor$

[Sin99]

Sao giống Bunhia v ạ 

[DOTOANNANG]

Xem ví dụ khác ở đây: 

 

$\lceil$ https://diendantoanh...ndpost&p=713632 $\rfloor$

Edited by DOTOANNANG, 19-11-2018 - 18:56.

[DOTOANNANG]

Xem ví dụ khác ở đây: https://diendantoanh...ndpost&p=713632

 

$\lceil$ https://diendantoanh...ndpost&p=710632 $\rfloor$

$\lceil$ https://diendantoanh...09979 $\rfloor$

[DOTOANNANG]

$$\sqrt{a+ b+ c}= \sqrt{\left ( a+ b+ c \right )\left ( \frac{a- 1}{a}+ \frac{b- 1}{b}+ \frac{c- 1}{c} \right )}\geqq \sqrt{a- 1}+ \sqrt{b- 1}+ \sqrt{c- 1}$$

 

$\lceil$ Bất đẳng thức Holder! $\rfloor$

 

$\lceil$ https://diendantoanh...ndpost&p=709563 $\rfloor$