\(B=\left|x-3\right|+\left|x-5\right|\)
Vì \(\left|x-3\right|,\left|x-5\right|\ge0\forall x\)
\(\Rightarrow\left|x-3\right|+\left|x-5\right|\ge0\forall x\)
\(\Rightarrow B\ge0\)
+) Nếu \(x< 3\Rightarrow\left|x-3\right|=3-x,\left|x-5\right|=5-x\)
\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=3-x+5-x=8-2x\)
TH1: Nếu \(x< 0\Rightarrow-x>0\Rightarrow B=8+2\left(-x\right)>8\)
TH2: Nếu \(x=0\Rightarrow B=8\)
TH3: Nếu \(0< x< 3\Rightarrow B=8-2x< 8\)
+) Nếu \(x=3\Rightarrow\left|x-3\right|=0,\left|x-5\right|=2\)
\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=2\)
+) Nếu \(3< x< 5\Rightarrow\left|x-3\right|=x-3,\left|x-5\right|=5-x\)
\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=x-3+5-x=2\)
+) Nếu \(x=5\Rightarrow\left|x-3\right|=2,\left|x-5\right|=0\)
\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=2\)
+) Nếu \(x>5\Rightarrow\left|x-3\right|=x-3,\left|x-5\right|=x-5\)
\(B=\left|x-3\right|+\left|x-5\right|=x-3+x-5=2x-8>2\)
\(\Rightarrow B_{max}>8\Leftrightarrow x< 0\)
