Giải pt

$3x^{4}-4x^{3}=1-\sqrt{(1+x^{2})^{3}}$

Giải pt
$\sqrt[3]{14-x^{2}}+x=2(1+\sqrt{x^{2}-2x-1})$

$\sqrt{5x^{2}-14x+9}-\sqrt{x^{2}-x-20}=5\sqrt{x+1}$

$\sqrt{x^{2}+9x-1}+x\sqrt{11-3x}=2x+3$

$2(x-2)(\sqrt[3]{4x-4}+\sqrt{2x-2})=3x-1$

$4\sqrt{x+2}+\sqrt{22-3x}=x^{2}+8$

Cho $a\geq b>0$
CMR: $\left ( 2^{a}+\frac{1}{2^{a}} \right )^{b}\leq \left ( 2^{b} +\frac{1}{2^{b}}\right )^{a}$
Đề thi khối D - 2007

Giải hệ phương trình
$1.\left\{\begin{matrix} x^{2}-2x+3=y^{2}-2y\\ y^{2}-2xy+2x+4=0 \end{matrix}\right.$

$2.\left\{\begin{matrix} \frac{x}{x^{2}-y}+\frac{5y}{x+y^{2}}=4\\ 5x+y+\frac{x^{2}-5y^{2}}{xy}=5 \end{matrix}\right.$

$3.\left\{\begin{matrix} 2x^{3}-(y+2)x^{2}+xy=-\frac{2}{5}\\ x^{2}+x-y=\frac{9}{5} \end{matrix}\right.$

$4.\left\{\begin{matrix} xy^{2}-2y+3x^{2}=0\\ y^{2}+x^{2}y+2x=0 \end{matrix}\right.$

$5.\left\{\begin{matrix} x^{3}+3xy^{2}=-49\\ x^{2}-8xy+y^{2}=8y-17x \end{matrix}\right.$