Question

найдите корни ур
авнения||х|-5|=6

Answer 1

$||x|-5|=6\\ \left [ \begin{gathered} \left\{{|x|-5\geq0}\atop { |x|-5=6}\right.\\ \left\{{|x|-5<0}\atop { 5-|x|=6}\right.\end{gathered}\right.\\ \left [ \begin{gathered} \left\{{|x|\geq5}\atop { |x|=11}\right.\\ \left\{{|x|<5}\atop { |x|=-1}\right.\end{gathered}\right.$

Вторая система решений не имеет, т.к. $|A|\geq0$

$\left\{ \left[ \begin{gathered} x\geq5\\ x\leq -5 \end{gathered} \right. \atop { |x|=11}\right.\\ \left\{\begin{gathered} \left[ \begin{gathered} x\geq5\\ x\leq -5 \end{gathered} \right.\\ \left[ \begin{gathered} x=11\\ x=-11 \end{gathered} \right. \end{gathered} \right.\\ Answer: \pm 11$