\[\boxed{\mathbf{518\ (518).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \sqrt{x^{2}} = x - 4\]
\[|x| = x - 4\]
\[x - x = - 4,\text{\ \ \ \ \ } - x - x = - 4\]
\[x = 2,\ \ но\ 2 \neq - 2.\]
\[Ответ:нет\ таких\text{\ \ x}.\]
\[2)\ \sqrt{x^{2}} = 6 - x\]
\[|x| = 6 - x\]
\[- x = 6 - x,\ \ 0 \neq 6\]
\[x = 6 - x,\ \ x = 3\]
\[Ответ:x = 3.\]
\[3)\ 2\sqrt{x^{2}} = x + 3\]
\[2|x| = x + 3\]
\[2x - x = 3,\ \ - 2x - x = 3\]
\[x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 1\]
\[Ответ:\ \ x = 3;\ x = - 1.\]
\[\boxed{\mathbf{51}\mathbf{8}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[|a| = a\ \ \ \ \ \ и\ \ \ \ \ \ \ |a| = - a\text{\ \ \ \ }\]
\[выполняется\ для\ нуля.\]