Question

Giải phương trình sau:

\(\left|x-1\right|+\left|x-2\right|=5\)

Answer 1

Ta xét các trường hợp :

TH1 : \(x< 1\Rightarrow x-1,x-2< 0\Rightarrow\left|x-1\right|=1-x;\left|x-2\right|=2-x\)

\(\Rightarrow1-x+2-x=5\Leftrightarrow2x=-2\Leftrightarrow x=-1\left(t.m\right)\)

TH2 : \(1\le x< 2\Rightarrow x-2< 0\le x-1\Rightarrow\left|x-1\right|=x-1;\left|x-2\right|=2-x\\ \Rightarrow x-1+2-x=5\Leftrightarrow1=5\left(VL\right)\)

TH3: \(x\ge2\Rightarrow x-1,x-2\ge0\Leftrightarrow\left|x-1\right|=x-1;\left|x-2\right|=x-2\)

\(\Rightarrow x-1+x-2=5\Leftrightarrow2x=8\Leftrightarrow x=4\left(t.m\right)\)