\(A=0,5-\left|x-3,5\right|\)
\(\left|x-3,5\right|\ge0\)
\(\Rightarrow A=0,5-\left|x-3,5\right|\le0,5\)
Dấu "=" xảy ra khi:
\(\left|x-3,5\right|=0\Rightarrow x-3,5=0\Rightarrow x=-3,5\)
\(B=-\left|1,4-x\right|\)
\(\left|1,4-x\right|\ge0\)
\(\Rightarrow B=-\left|1,4-x\right|\le0\)
Dấu "=" xảy ra khi:
\(1,4-x=0\Rightarrow x=1,4\)
2)
\(A=17+\left|3,4-x\right|\)
\(\left|3,4-x\right|\ge0\)
\(\Rightarrow A=17+\left|3,4-x\right|\ge17\)
Dấu "=" xảy ra khi:
\(3,4-x=0\Rightarrow x=3,4\)
\(B=\left|2x+\dfrac{1}{2}\right|-3,08\)
\(\left|2x+\dfrac{1}{2}\right|\ge0\)
\(B_{MIN}\Rightarrow\left|2x+\dfrac{1}{2}\right|_{MAX}=0\)
\(B_{MIN}=-3,08\) khi \(2x+\dfrac{1}{2}=0\Rightarrow2x=-\dfrac{1}{2}\Rightarrow x=-\dfrac{1}{4}\)
\(\text{Câu 1 : }\)
\(\text{a) }A=0.5-\left|x-3.5\right|\\ \text{Ta có : }\left|x-3.5\right|\ge0\\ \Leftrightarrow0.5-\left|x-3.5\right|\le0.5\\ \text{Dấu }"="\text{ xảy ra khi : }\\ \left|x-3.5\right|=0\\ \Leftrightarrow x-3.5=0\\ \Leftrightarrow x=3.5\\ \text{Vậy }A_{\left(Max\right)}=0.5\text{ khi }x=3.5\)
\(\text{b) }B=-\left|1.4-x\right|\\ \text{Ta có : }\left|1.4-x\right|\ge0\\ \Leftrightarrow-\left|1.4-x\right|\le0\\ \text{Dấu }"="\text{ xảy ra khi : }\\ -\left|1.4-x\right|=0\\ \Leftrightarrow\left|1.4-x\right|=0\\ \Leftrightarrow1.4-x=0\\ \Leftrightarrow x=1.4\\ \text{Vậy }B_{\left(max\right)}=0\text{ khi }x=1.4\)
\(\text{Câu 2 : }\)
\(\text{a) }A=17+\left|3.4-x\right|\\ \text{Ta có : }\left|3.4-x\right|\ge0\\ \Leftrightarrow17+\left|3.4-x\right|\ge17\\ \text{Dấu }"="\text{xảy ra khi : }\\ \left|3.4-x\right|=0\\ \Leftrightarrow3.4-x=0\\ \Leftrightarrow x=3.4\\ \text{Vậy }A_{\left(Min\right)}=17\text{ khi }x=3.4\)
\(\text{b) }\left|2x+\dfrac{1}{2}\right|-3.08\\ \text{Ta có : }\left|2x+\dfrac{1}{2}\right|\ge0\\ \left|2x+\dfrac{1}{2}\right|-3.08\ge-3.08\\ \text{Dấu }"="\text{xảy ra khi : }\\ \left|2x+\dfrac{1}{2}\right|=0\\ \Leftrightarrow2x+\dfrac{1}{2}=0\\ \Leftrightarrow2x=-\dfrac{1}{2}\\ \Leftrightarrow x=-1\\ \text{Vậy }B_{\left(Min\right)}=-3.08\text{ khi }x=-1\)
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