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a) \(|\dfrac{3}{5}x|=|-\dfrac{1}{6}|\)
\(\Rightarrow|\dfrac{3}{5}x|=\dfrac{1}{6}\)
\(\Rightarrow\dfrac{3}{5}x=\dfrac{1}{6}\) hoặc \(\dfrac{3}{5}x=-\dfrac{1}{6}\)
\(\Rightarrow x=\dfrac{1}{6}:\dfrac{3}{5}\) hoặc \(x=-\dfrac{1}{6}:\dfrac{3}{5}\)
\(\Rightarrow x=\dfrac{1}{6}.\dfrac{5}{3}\) hoặc \(x=-\dfrac{1}{6}.\dfrac{5}{3}\)
\(\Rightarrow x=\dfrac{5}{18}\) hoặc \(x=-\dfrac{5}{18}\)
b) \(|2x-3|+0,5=\dfrac{1}{3}:2\)
\(\Rightarrow|2x-3|+\dfrac{1}{2}=\dfrac{1}{3}.\dfrac{1}{2}\)
\(\Rightarrow|2x-3|+\dfrac{1}{2}=\dfrac{1}{6}\)
\(\Rightarrow|2x-3|=\dfrac{1}{6}-\dfrac{1}{2}=-\dfrac{1}{3}\)
Vì \(|2x-3|\ge0\forall x\)
=> Không tồn tại x thỏa mãn
c)\(|x-\dfrac{5}{6}|=2\left(x+\dfrac{1}{2}\right)\)
\(\Rightarrow|x-\dfrac{5}{6}|=2x+1\)
\(\Rightarrow x-\dfrac{5}{6}=2x+1\) hoặc \(x-\dfrac{5}{6}=-2x-1\)
\(\Rightarrow-\dfrac{5}{6}-1=2x-x\) hoặc \(-\dfrac{5}{6}+1=-2x-x\)
\(\Rightarrow-\dfrac{11}{6}=x\) hoặc \(\dfrac{1}{6}=-3x\)
\(\Rightarrow x=-\dfrac{11}{6}\) hoặc \(x=\dfrac{1}{6}:\left(-3\right)=\dfrac{1}{6}.\left(\dfrac{1}{-3}\right)=\dfrac{1}{-18}\)
Bài 2 : Bài giải
a, \(2008^n=1=2008^0\)
\(\Rightarrow\text{ }n=0\)
b, \(32^{-n}\cdot16^n=1024\)
\(\left(2^5\right)^{-n}\cdot\left(2^4\right)^n=2^{10}\)
\(2^{-5n}\cdot2^{4n}=2^{10}\)
\(2^{-n}=2^{10}\)
\(\Rightarrow\text{ }n=-10\)
c, \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^n=\frac{4\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2^6\cdot2^6=2^{12}\)
\(\Rightarrow\text{ }n=12\)
\(\left(x-3\right)^6-1\dfrac{1}{3}=62\dfrac{1}{4}\)
\(\left(x-3\right)^6-\dfrac{4}{3}=\dfrac{249}{4}\)
\(\left(x-3\right)^6=\dfrac{249}{4}-\dfrac{4}{3}\)
\(\left(x-3\right)^6=\dfrac{747}{12}-\dfrac{16}{12}\)
\(\left(x-3\right)^6=\dfrac{731}{12}\)
A=1.2.3+2.3.4+3.4.5+...+98.99.100
Khi \(|x|>3:M=\frac{6}{|x|-3}>0\)
Khi \(0\le|x|< 3\Leftrightarrow-3\le|x|-3< 0:-6\le M=\frac{6}{|x|-3}\le-2\)( vì \(x\in Z\))
Vậy GTNN của M là -6 khi x = 2 hoặc x = -2.
\(m=\sqrt[3]{6}\)
`m^3=6`
`to m=\(\sqrt[3]{6}\)