\(\ln (6-x) \cdot \ln (2 x+1)=\ln (6-x) \cdot \ln (x-2)\)

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

\(\sqrt{-2 \sin x+\cos x}=\sqrt{-2 \cos x+\sin x}\)

\(\left|x^2-1\right|=|x+1| \sqrt{3 x+1}\)

\(\sqrt{4 x-1} \ln \left(x^2-2 x+1\right)=0\)

\(\left|\cos ^2 x+2 \sin x-2\right|=\cos ^2 x+\sin x+2\)

\(\left|x^2-1\right|+8=|x+1|+8|x-1|\)

\((x+1)^2-2|x+1|+1=0\)

\(\left|x^2+2 x+7\right|=\left|x^2-2 x-7\right|\)

\(\left\{\begin{array}{l}\sqrt{2 x-x^2}=\sqrt{4 y-4 y^2} \\ y=x^2\end{array}\right.\)

\(\left\{\begin{array}{l}\sqrt{4-y^2}=\sqrt{4-4 x^2} \\ x y+4=2 x+2 y\end{array}\right.\)

\(\left\{\begin{array}{l}\log _3\left(2-x^2\right)=\log _3\left(2-y^2\right) \\ x^2+y^2=4 x+6 y\end{array}\right.\)

\(\log _4(2 x-1) \cdot \sqrt{x^2-4 x+3}=0\)

\(\left|x^2-1\right|=|x+1| \sqrt{x^2-x+4}\)