Tìm x $\left| \left| x-1 \right|-5 \right|=3$

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1. Đáp án:

    

   Giải thích các bước giải:

    ||x-1| – 5 | = 3

   ↔ \(\left[ \begin{array}{l}|x-1|-5=3\\|x-1|-5=-3\end{array} \right.\)

   ↔ \(\left[ \begin{array}{l}|x-1|=3+5\\|x-1|x=-3+5\end{array} \right.\)

   ↔ \(\left[ \begin{array}{l}|x-1|=8\\|x-1|=2\end{array} \right.\)

   ↔  \(\left[ \begin{array}{l}x-1=8\\x-1=-8\\x-1=2\\x-1=-2\end{array} \right.\)

   ↔ \(\left[ \begin{array}{l}x=8+1\\x=-8+1\\x=2+1\\x=-2+1\end{array} \right.\)

   ↔ \(\left[ \begin{array}{l}x=9\\x=-7\\x=3\\x=-1\end{array} \right.\) 

   Vậy x ∈ { -7 ; -1 ; 3 ; 9 }

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2. Giải thích các bước giải:

   $ \begin{array}{l}||x-1|-5|=3\\⇒|x-1|-5=±3\\⇒\left[ \begin{array}{l}|x-1|-5=3\\|x-1|-5=-3\end{array} \right.⇒\left[ \begin{array}{l}|x-1|=8\\|x-1|=2\end{array} \right.\\\left[ \begin{array}{l}\left[ \begin{array}{l}x-1=8\\x-1=-8\end{array} \right.\\\left[ \begin{array}{l}x-1=2\\x-1=-2\end{array} \right.\end{array} \right.⇒\left[ \begin{array}{l}\left[ \begin{array}{l}x=9\\x=-7\end{array} \right.\\\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\end{array} \right.\end{array}.$

   Vậy $x∈\{-7;-1;3;9\}$

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