Ta có:\(\left|x-1\right|\ge0;\forall x\)
\(\left|x+2\right|\ge0;\forall x\)
\(\left|x-3\right|\ge0;\forall x\)
\(\left|x+4\right|\ge0;\forall x\) ......
Cộng tất cả ta được:
\(\left|x-1\right|+\left|x+2\right|+\left|x-3\right|+\left|x+4\right|+...+\left|x-9\right|\ge0\)
\(\Rightarrow Min_T=0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}x=1\\x=-2\\x=3\\x=-4.....\end{matrix}\right.\)
\(T=\left|9-x\right|+\left|x+8\right|+...+\left|3-x\right|+\left|x+2\right|+\left|x-1\right|\)
\(T\ge\left|9-x+x+8\right|+\left|7-x+x+6\right|+...+\left|3-x+x+2\right|+\left|x-1\right|\)
\(T\ge17+13+9+5+\left|x-1\right|\)
\(T\ge44+\left|x-1\right|\ge44\)
\(T_{min}=44\) khi \(x=1\)
