User:Luosiji/Sandbox

$20x^{2}+2y^{2}-5=0\!$

$36x^{2}+68xy+36y^{2}-136x-144y+139=0\!$

$y-{\frac {|x|}{12}}=-{\frac {4}{5}}{\sqrt[{3}]{\left(\left|x\right|+{\frac {y}{12}}-{\frac {9}{4}}\right)^{2}}}+2\!$

$y-{\frac {|x|}{6}}={\frac {1}{2}}{\sqrt[{3}]{\left(\left|\left|x\right|+{\frac {y}{6}}-{\frac {9}{4}}\right|-1\right)^{2}}}-{\frac {6}{5}}\!$

${\sqrt[{3}]{x^{2}}}\pm {\sqrt {9-x^{2}}}\!$

$\sum _{i=0}^{n}\sum _{j=1}^{m}{m \choose j}{i}^{m-j}={\left(n+1\right)}^{m}$

$\sum _{i=0}^{n}{\left(i+1\right)}^{m}-{i}^{m}={\left(n+1\right)}^{m}$

$E[T]\leq \lfloor \log _{n}m\rfloor +1+{\frac {m-1}{m}}{\frac {n}{n-1}}.$