IDT

$\left\{\begin{matrix} \sqrt{1-x^{2}}-\sqrt{y\sqrt{y}+1}-\sqrt{y}=x\\ (4x+3)(\sqrt{4-\sqrt{y}}+\sqrt[3]{3x+8})=9 \end{matrix}\right.$

$\left\{\begin{matrix} \frac{1}{\sqrt{x+2y^{2}}}+\frac{1}{\sqrt{y+2x^{2}}}=\frac{2\sqrt{2}}{\sqrt{(x+y)(x+y+1)}}\\ \frac{\sqrt{x}+\sqrt{y}}{2}+\sqrt{y^{2}-2}=2\sqrt[4]{y(x^{2}-2)} \end{matrix}\right.$

$4x\sqrt{x^{2}-1}-\sqrt{x(x^{2}+8)}=4x^{2}-x-6$

$25x+9\sqrt{9x^{2}-4}=\frac{2}{x}+\frac{18x}{x^{2}+1}$

Cho $a, b, c$ là 3 số thực dương và $a+b+c=1$. Chứng minh

$\frac{a^{4}}{b(1-c)}+\frac{b^{4}}{c(1-a)}+\frac{c^{4}}{a(1-b)}+3(ab+bc+ca)\geqslant 1$