\(\left|4x\right|-\left|-13,5\right|=\left|-7,5\right|\)
\(\Rightarrow\left|4x\right|-13,5=7,5\)
\(\Rightarrow\left|4x\right|=21\)
\(\Rightarrow\left[{}\begin{matrix}4x=21\\4x=-21\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{21}{4}\\x=\dfrac{-21}{4}\end{matrix}\right.\)
\(\left|x-3,4\right|+\left|2,6-y\right|=0\)
\(\left\{{}\begin{matrix}\left|x-3,4\right|\ge0\forall x\\\left|2,6-y\right|\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left|x-3,4\right|+\left|2,6-y\right|\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left|x-3,4\right|=0\Rightarrow x=3,4\\\left|2,6-y\right|=0\Rightarrow y=2,6\end{matrix}\right.\)
\(A= \left|x-500\right|+ \left|x-300\right|\)
\(A= \left|x-500\right|+\left|300-x\right|\)
Áp dụng bất đẳng thức:
\(\left|A\right|+\left|B\right|\ge\left|A+B\right|\)
\(A\ge\left|x-500+300-x\right|\)
\(A\ge200\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-500\ge0\Rightarrow x\ge500\\300-x\ge0\Rightarrow x\le300\end{matrix}\right.\\\left\{{}\begin{matrix}x-500< 0\Rightarrow x< 500\\300-x< 0\Rightarrow x>300\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow300< x< 500\)
B1: \(\left|4x\right|-\left|-13.5\right|=\left|-7,5\right|\)
\(\Leftrightarrow\left|4x\right|-13,5=7,5\)
\(\left|4x\right|=7,5+13,5\)
\(\Rightarrow\left|4x\right|=21\)
\(\Rightarrow x\pm21\)
\(\cdot4x=21\)
\(x=21:4\)
\(x=\dfrac{21}{4}\)
\(\cdot4x=-21\)
\(x=-21:4\)
\(x=\dfrac{-21}{4}\)
\(Vậy\) \(x\)\(\in\)\(\left\{\dfrac{21}{4};\dfrac{-21}{4}\right\}\)
B2:
\(\left|x-3,4\right|+\left|2,6-y\right|=0\)
\(\Rightarrow\)... tự làm nhé bạn
