Help meeeeeee!!!!!!!
\(a,B=\left|x-2017\right|+\left|x-2016\right|\)
\(=\left|x-2017\right|+\left|2016-x\right|\)
Áp dụng t.c \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\) ta có:
\(\left|x-2017\right|+\left|2016-x\right|\ge\left|x-2017+2016-x\right|\)
Hay \(B\ge1\) với mọi x
Để B=1 thì:
\(\left\{{}\begin{matrix}x-2017\ge0\\2016-x\ge0\end{matrix}\right.\Leftrightarrow2016\le x\le2017\)
Vậy...
\(b,C=\left|x+5\right|+\left|x+3\right|\)
\(=\left|x+5\right|+\left|-x-3\right|\)
Áp dụng t/c \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\) ta có:
\(\left|x+5\right|+\left|-x-3\right|\ge\left|x+5-x-3\right|\)
Hay \(C\ge2\) với mọi x
Để C=2 thì:
\(\left\{{}\begin{matrix}x+5\ge0\\-x-3\ge0\end{matrix}\right.\Leftrightarrow-5\le x\le-3\)
Vậy...