2 replies to this topic

[pmhung512]

B1.Cho $a,b,c,d> 0$ thỏa mãn $c+d< a+b$
CMR:$\frac{c^{2}}{c+d}+\frac{(a-c)^{2}}{a+b-c-d}\geq \frac{a^{2}}{a+b}$

B2.CM: $\sqrt{5+5x^{2}}+\left | 2-x \right |\geq 4$

B3.Cho $a,b,c> 0$ thỏa mãn $\frac{a}{m}+\frac{b}{n}+\frac{c}{p}=1$
CMR: $m+n+p\geq(\sqrt{a}+\sqrt{b}+\sqrt{c})^{2}$
 

[baotranthaithuy]

1.

$\frac{c^{2}}{c+d}+\frac{(a-c)^{2}}{a+b-c-d}\geq \frac{(c+a-c)^{2}}{c+d+a+b-c-d}=\frac{a}{b+a}$

[Hoang Long Le]

 

B2.CM: $\sqrt{5+5x^{2}}+\left | 2-x \right |\geq 4$

B3.Cho $a,b,c> 0$ thỏa mãn $\frac{a}{m}+\frac{b}{n}+\frac{c}{p}=1$
CMR: $m+n+p\geq(\sqrt{a}+\sqrt{b}+\sqrt{c})^{2}$
 

2. $VT=\sqrt{4x^2-4x+1+x^2+4x+4}+|2-x|=\sqrt{(2x-1)^2+(x+2)^2}+|2-x|\geq |x+2|+|2-x|\geq 4$

3. Ta có: $1=\sum \frac{a}{m}\geq \frac{(\sum \sqrt{a})^2}{\sum m}\Rightarrow \sum m\geq (\sum \sqrt a)^2$

Edited by Hoang Long Le, 03-01-2015 - 17:07.