thuy99

mn cho ý kiên ạ

cho các số thực dương a, b, c thỏa $abc\geq1$

$\frac{a^4b^2c^2}{bc+1}+\frac{b^4a^2c^2}{ac+1}+\frac{c^4b^2a^2}{ab+1}\geq \frac{3}{2}$

gpt

$2sin^3\left ( x-\frac{\pi}{6} \right )+6sin^3\left (x+\frac{\pi}{3} \right )=\left ( \frac{1}{\sqrt{3}}+9 \right )cosx.sin2x$

$cos3x+cosx-cos2x=\frac{1}{2}$

1. cho a,b,c >0 thỏa $a^2+b^2+c^2+ab-2bc-2ca=0$

cmr $\frac{c^2}{(a+b-c)^2}+\frac{c^2}{a^2+b^2}+\frac{\sqrt{ab}}{a+b}\geq 2$

2. cho a,b,c >0 thỏa $(a+c)(b+c)=4c^2$

cmr $\frac{4a}{b+c}+\frac{4b}{a+c}-\frac{2ab}{c^2}-\frac{\sqrt{7c^2-3a}}{c}\geq 4$

3. cho a,b,c> 0 thỏa $a\geq b\geq c$ tìm min

$P=\frac{(a^2+c^2)\sqrt{ab+bc+ca}}{ac(a+b+c)}+\sqrt{\frac{a^2+c^2}{2bc}}$

4. cho x,y,z thực $\epsilon \left [ 1;4 \right ]$ và $x\ge y,x\ge z$

tìm min $P=\frac{x}{2x+3y}+\frac{y}{y+z}+\frac{z}{z+x}$