Question

Tìm x, biết: |x - 5| - |x - 1| = 5

Answer 1

\(\left[{}\begin{matrix}x-5-x+1-5=0\\x-5-x+1+5=0\end{matrix}\right.\)vô nghiệm

Answer 2

TH1: \(x\ge5\)

\(pt\Leftrightarrow x-5-x+1=5\Leftrightarrow-4=5\left(VLý\right)\)

TH2: \(5>x\ge1\)

\(pt\Leftrightarrow5-x-x+1=5\Leftrightarrow2x=1\Leftrightarrow x=\dfrac{1}{2}\left(ktm\right)\)

TH3: \(x< 1\)

\(pt\Leftrightarrow5-x+x-1=5\Leftrightarrow4=5\left(VLý\right)\)

Vậy \(S=\varnothing\)