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a) \(\left|x-7\right|+\left|x+5\right|=\left|7-x\right|+\left|x+5\right|\ge\left|7-x+x+5\right|=12\)
Dấu "=" xảy ra khi \(-5\le x\le7\)
b) Đặt \(\left|2x-1\right|=t\left(t\ge0\right)\)
ta được \(t^2-3t+2=\left(t^2-2.\frac{3}{2}.x+\frac{9}{4}\right)-\frac{1}{4}=\left(t-\frac{3}{2}\right)^2-\frac{1}{4}\ge-\frac{1}{4}\)
Dấu "=" xảy ra khi \(\left(t-\frac{3}{2}\right)^2=0\Leftrightarrow t-\frac{3}{2}=0\Leftrightarrow t=\frac{3}{2}\Leftrightarrow\left|2x-1\right|=\frac{3}{2}\)
<=>\(\orbr{\begin{cases}2x-1=-\frac{3}{2}\\2x-1=\frac{3}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=-\frac{1}{2}\\2x=\frac{5}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{4}\\x=\frac{5}{4}\end{cases}}\)
Vậy...........
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\(\left|2x-1\right|+\left|2x-3\right|=\left|2x-1\right|+\left|3-2x\right|\)
\(\Rightarrow A=\left|2x-1\right|+\left|3-2x\right|\ge\left|2x-1+3-2x\right|\)
\(\Rightarrow A=\left|2x-1\right|+\left|3-2x\right|\ge\left|2\right|=2\)
dấu "="xảy ra khi \(\left(2x-1\right).\left(3-2x\right)\ge0\)
\(\Rightarrow\frac{1}{2}\le x\le\frac{3}{2}\)
vậy min A=2 khi \(\frac{1}{2}\le x\le\frac{3}{2}\)
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>: đang làm, nghịch ngu nhấn lung tung....h làm lại T.T
\(A=\left|x+1\right|+\left|2x+5\right|\ge\left|x+1+2x+5\right|=\left|3x+6\right|\)
Dấu = xảy ra khi \(\left(x+1\right).\left(2x+5\right)\ge0\)
\(\Rightarrow-\frac{5}{2}\le x\le-1\)
\(\left|3x+6\right|+\left|3x+8\right|=\left|-3x-6\right|+\left|3x+8\right|\ge\left|-3x-6+3x+8\right|=2\)
dấu = xảy ra khi \(\left(-3x-6\right).\left(3x+8\right)\ge0\)
\(\Rightarrow-\frac{8}{3}\le x\le-2\)
\(A\ge2\Leftrightarrow-\frac{8}{3}\le x\le-2\)
Vậy...
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Ta co: |1-2x|>hoac bang 0
suy ra 3. |1-2x|>hoac bang 0
3. |1-2x|-5> hoac bang -5
Dau "='' xay ra khi 1-2x=0 hay x=1/2
Vay Min A=-5 khi x= 1/2