a/ Vỡi mọi x ta có :
\(\left|x-3\right|\ge0\)
\(\Leftrightarrow\left|x-3\right|+50\ge50\)
\(\Leftrightarrow A\ge50\)
Dấu "=" xảy ra khi :
\(\left|x-3\right|=0\)
\(\Leftrightarrow x=3\)
Vậy \(A_{Min}=50\Leftrightarrow x=3\)
b/ Với mọi x ta có :
\(\left|x+8\right|\ge0\)
\(\Leftrightarrow2014-\left|x+8\right|\le2014\)
\(\Leftrightarrow B\le2014\)
Dấu "=" xảy ra khi :
\(\left|x+8\right|=0\)
\(\Leftrightarrow x=-8\)
Vậy \(B_{Max}=2014\Leftrightarrow x=-8\)
c, Với mọi x,y ta có :
\(\left\{{}\begin{matrix}\left|x-100\right|\ge0\\\left|y+2014\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left|x-100\right|+\left|y+2014\right|\ge0\)
\(\Leftrightarrow\left|x-100\right|+\left|y+2014\right|-2015\ge-2015\)
\(\Leftrightarrow C\ge-2015\)
Dấu "=" xảy ra khi :
\(\left\{{}\begin{matrix}\left|x-100\right|=0\\\left|y+2014\right|=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=100\\y=-2014\end{matrix}\right.\)
Vậy \(C_{Min}=-2015\Leftrightarrow\left\{{}\begin{matrix}x=100\\y=-2014\end{matrix}\right.\)
a/ Vỡi mọi x ta có :
|x−3|≥0|x−3|≥0
⇔|x−3|+50≥50⇔|x−3|+50≥50
⇔A≥50⇔A≥50
Dấu "=" xảy ra khi :
|x−3|=0|x−3|=0
⇔x=3⇔x=3
Vậy AMin=50⇔x=3AMin=50⇔x=3
b/ Với mọi x ta có :
|x+8|≥0|x+8|≥0
⇔2014−|x+8|≤2014⇔2014−|x+8|≤2014
⇔B≤2014⇔B≤2014
Dấu "=" xảy ra khi :
|x+8|=0|x+8|=0
⇔x=−8⇔x=−8
Vậy BMax=2014⇔x=−8BMax=2014⇔x=−8
c, Với mọi x,y ta có :
{|x−100|≥0|y+2014|≥0{|x−100|≥0|y+2014|≥0
⇔|x−100|+|y+2014|≥0⇔|x−100|+|y+2014|≥0
⇔|x−100|+|y+2014|−2015≥−2015⇔|x−100|+|y+2014|−2015≥−2015
⇔C≥−2015⇔C≥−2015
Dấu "=" xảy ra khi :
{|x−100|=0|y+2014|=0{|x−100|=0|y+2014|=0 ⇔{x=100y=−2014⇔{x=100y=−2014
Vậy CMin=−2015⇔{x=100y=−2014
a) Với mọi x ta có:
\(|x-3|\ge0\)
\(\Leftrightarrow|x-3|+50\ge50\)
\(\Leftrightarrow A\ge50\)
dấu" = "sẽ sảy ra khi:
\(|x-3|\ge0\)
\(\Leftrightarrow x=3\)
Vậy \(A_{min}=50\)
\(\Leftrightarrow x=3\)