quynhhph1

1) $16x^{3}+(8x^{2}-1)\sqrt{4x^{2}+1}=\frac{15}{16x+9}$

2) $(1+\sqrt{\frac{7}{3}x^{3}+\frac{2}{3}x+1})^{3}=\frac{11x^{3}+70x^{2}}{3}$

$1)$ $Cho$ $a \epsilon \begin{bmatrix} -1, 1 \end{bmatrix}$

Tìm min S = $a^{5}-3a^{4}+a^{3}+8a^{2}-14a+\frac{1}{a^{3}-a^{2}-3a+4}$

$2)$ $a,b,c>0$ và $a=max\begin{Bmatrix} a,b,c \end{Bmatrix}$

Tìm min $S=\frac{a}{b}+2\sqrt{1+\frac{b}{c}}+3\sqrt[3]{1+\frac{c}{a}}$ 

$3)$ $T=\begin{bmatrix} \frac{a}{(a-b)(ab-1)} \end{bmatrix}^{2} +\begin{bmatrix} \frac{b}{(a-b)(a^{2}-1)} \end{bmatrix}^{2}+\begin{bmatrix} \frac{a^{3}b}{(ab-1)(a^{2}-1)}\end{bmatrix}^{2}$

Cmr $T^{2}+3T^{-1}>10$

$1) a,b,c\geq 0; c\leq a\leq b$

Tìm GTNN $S=\frac{1}{a^{2}+c^{2}}+\frac{1}{b^{2}+c^{2}}+\sqrt{a+b+c}$

$2) a,b,c >0; a+b+c=1$

Tìm GTLN $T = \frac{4}{a+b}+\frac{4}{c+b}+\frac{4}{a+c}-\frac{1}{a}-\frac{1}{b}-\frac{1}{c}$

$\sqrt{x}\geq \frac{x^{4}- 2x^{3}+2x-1}{x^{3}-2x^{2}+2x}$

Cho $\frac{1}{\sqrt{x}+\sqrt{y}}+\frac{1}{\sqrt{y}+\sqrt{z}}+\frac{1}{\sqrt{z}+\sqrt{x}}=3$

Tìm max $A=\frac{1}{2\sqrt{x}+3\sqrt{y}+3\sqrt{z}}+\frac{1}{2\sqrt{y}+3\sqrt{x}+3\sqrt{z}}+\frac{1}{3\sqrt{x}+3\sqrt{y}+2\sqrt{z}}$