\(\left|\left|x-2017\right|+1\right|=30\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-2017\right|+1=-30\\\left|x-2017\right|+1=30\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-2017\right|=-31\\\left|x-2017\right|=29\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\in\varnothing\\\left\{{}\begin{matrix}x-2017=-29\\x-2017=29\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=1998\\x=2046\end{matrix}\right.\)
Vậy.............
Chúc bạn học tốt!!!
Ta có : $||x-2017|+1|=30$
\(=>\left[{}\begin{matrix}\left|x-2017\right|+1=30=>\left|x-2017\right|=29\\\left|x-2017\right|+1=-30\left(loại\right)\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}x-2017=29\\x-2017=-29\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}x=2046\\x=1988\end{matrix}\right.\)
| \(\left|x-2017\right|\) \(+1\) | \(=30\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-2017\right|+1=30\\\left|x-2017\right|+1=-30\end{matrix}\right.\)
\(TH1:\left|x-2017\right|+1=30\)
\(\Leftrightarrow\left|x-2017\right|=29\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2017=29\\x-2017=-29\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2046\\x=1988\end{matrix}\right.\)
\(TH2:\left|x-2017\right|+1=-30\)
\(\Leftrightarrow\left|x-2017\right|=-31\)
\(\rightarrow loại\) (do \(\left|x-2017\right|\ge0\))
Vậy \(x\in\left\{2046;1988\right\}\)
| |x - 2017 | + 1 | = 30
TH1: | x - 2017 | + 1 = -30
=> | x - 2017 | = - 31
=> x \(\in\varnothing\)
TH2: | x - 2017 | + 1 = 30
=> | x - 2017 | = 29
=> \(\left[{}\begin{matrix}x-2017=29\\x-2017=-29\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2046\\x=1988\end{matrix}\right.\)
\(\left|\left|x-2017\right|+1\right|=30\)
\(\Rightarrow\left[{}\begin{matrix}\left|x-2017\right|+1=30\\\left|x-2017\right|+1=-30\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left|x-2017\right|=29\\\left|x-2017\right|=-31\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-2017=29\\x-2017=-29\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2046\\x=1988\end{matrix}\right.\)
