$\sqrt{2x+4}-2\sqrt{2-x}=\frac{6x-4}{\sqrt{x^2+4}}$ \begin{array}{c}\sqrt{x+10}+\sqrt{y-1}=11\\ \sqrt{y+10}+\sqrt{x-1}=11\end{array}$$ \sqrt{x-2}+\sqrt{10-x}=x^2-12x+40$$ a)\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}$$ b)\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}$$ c)\sqrt{9-2\sqrt{14}}-\sqrt{9-2\sqrt{14}}$$ d)\sqrt{2(4-\sqrt{7})}$$ e)\sqrt{a+1+2\sqrt{a}}$$ f)-\sqrt{2(2-\sqrt{3})}+\sqrt{2(2+\sqrt{3})}$$ g)\sqrt{x+y-2\sqrt{xy}}$$ (x\ge y)$$ h)\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$$ i)\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}$$ j)\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5-2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}-\sqrt{7+2\sqrt{10}}}}$$ k)\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}$$ l)\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}$$ m\left)\right(4+\sqrt{15}\left)\right(\sqrt{10}-\sqrt{6}\left)\right(4-\sqrt{15})$$ n\left)\sqrt{3-\sqrt{5}}\right(\sqrt{10}-\sqrt{2}\left)\right(3+\sqrt{5})$$ o)\sqrt{31+2}.\sqrt{6+\sqrt{5+\sqrt{2}}}.+\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}$$ a)x-\sqrt{x}$$ b)x-1$$ c)x-2\sqrt{2}+1$$ d)-x+3\sqrt{x}+4$$ e)2x-\sqrt{x}-1$$ f)x-\sqrt{2}-2$$ g)x\sqrt{x}+1$$ h)2x+\sqrt{x}-3$$ i)x\sqrt{x}+9x+14\sqrt{x}$$ j)2x\sqrt{x}+5x+3\sqrt{x}$$ E=(\frac{3x-2}{x^2-9}-\frac{5x+1}{x^2-3x}-\frac{x+1}{x^2+3x}):\frac{x+2}{x^2+3x}-\frac{4^2-2x}{x^2-x-6}$\{\begin{array}{c}{x}^3+x-2=y^3+3y^2+4y\\ x^5+y^3+1=0\end{array}$ \frac{2\sqrt{x}}{x+1}$$ \sqrt{p}$$ \sqrt{3x-1}-\sqrt{x+1}=3x^2-2x-1$$ (x+1)\sqrt{x^2-5x+3}=x^2+1$$ x^2+4x+5=2\sqrt{2x+3}$$ a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}{b}^2-...+a^2{b}^{n-3}-a{b}^{n-2}+b^{n-1})$$ x^3+y^3-3xy\left(x^2+y^2\right)+4x^2{y}^2\left(x+y\right)-4x^3{y}^3=0$$ a,b,c,d>0$$ \frac{a-d}{b+d}+\frac{d-b}{b+c}+\frac{b-c}{c+a}+\frac{c-a}{a+d}\ge 0$$ \left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$ \left(1-\frac{2-\sqrt{2}}{1-\sqrt{2}}\right)$$ \frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}$$ \frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}$$ \frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}$$ \left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)$$ \frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}$$ \frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{3\sqrt{z}}{\sqrt{xz}+3\sqrt{z}+3}$$ \sqrt{10P-1}$$