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\(b,\Rightarrow\dfrac{x}{2}-\dfrac{3x}{5}-\dfrac{13}{5}=-\dfrac{7}{5}-\dfrac{7x}{10}\\ \Rightarrow\dfrac{1}{2}x-\dfrac{3}{5}x+\dfrac{7}{10}x=\dfrac{6}{5}\\ \Rightarrow\dfrac{3}{5}x=\dfrac{6}{5}\Rightarrow x=2\\ c,\Rightarrow\dfrac{2x-3}{3}-\dfrac{5-3x}{6}=-\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{7}{6}\\ \Rightarrow\dfrac{4x-6-5+3x}{6}=\dfrac{7}{6}\\ \Rightarrow7x-11=7\Rightarrow x=\dfrac{18}{7}\\ d,\Rightarrow\dfrac{2}{3x}+\dfrac{7}{x}=\dfrac{4}{5}+2+\dfrac{3}{12}=\dfrac{61}{20}\\ \Rightarrow\dfrac{23}{3x}=\dfrac{61}{20}\\ \Rightarrow183x=460\\ \Rightarrow x=\dfrac{460}{183}\\ e,\Rightarrow2\left(x-1\right)-\left(x-1\right)^2=0\\ \Rightarrow\left(x-1\right)\left(2-x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
e: Ta có: \(\left(x-1\right)^2=2\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
a: =>2(2x-3)-9=5-3x-2
=>4x-6-9=-3x+3
=>4x-15=-3x+3
=>7x=18
=>x=18/7
b: =>\(\dfrac{2}{3x}-\dfrac{3}{12}=\dfrac{4}{5}-\dfrac{21}{3x}+2\)
=>\(\dfrac{23}{3x}=\dfrac{4}{5}+2+\dfrac{1}{4}=\dfrac{61}{20}\)
=>3x=460/61
=>x=460/183
2: (3x-4)^2+2>=2
=>5/(3x-4)^2+2<=5/2
=>B>=-5/2
Dấu = xảy ra khi x=4/3
4: D=(3x^2+7-4)/(3x^2+7)=1-4/3x^2+7
3x^2+7>=7
=>4/3x^2+7<=4/7
=>-4/3x^2+7>=-4/7
=>D>=3/7
Dấu = xảy ra khi x=0
2) B = \(\dfrac{-5}{\left(3x-4\right)^2+2}\)
Ta có: ( 3x-4)2 \(\ge\) 0 , \(\forall\) x
=> ( 3x-4)2 +2 \(\ge\) 2, \(\forall\) x
=> \(\dfrac{1}{\left(3x-4\right)^2+2}\) \(\le\) \(\dfrac{1}{2}\) , \(\forall\) x
=> \(\dfrac{-5}{\left(3x-4\right)^2+2}\) \(\ge\) \(\dfrac{-5}{2}\) , \(\forall\) x
=> B \(\ge\) \(\dfrac{-5}{2}\)
Vậy B đạt GTNN khi bằng \(\dfrac{-5}{2}\)
Dấu "= " xảy ra khi 3x - 4 = 0
4) D=\(\dfrac{3x^2+3}{3x^2+7}\)
= 1 - \(\dfrac{4}{3x^2+7}\)
Ta có: 3x2 \(\ge\) 0, \(\forall\) x
=> 3x2 +7 \(\ge\) 7, \(\forall\) x
=> \(\dfrac{1}{3x^2+7}\) \(\le\) \(\dfrac{1}{7}\)
=> \(\dfrac{4}{3x^2+7}\) \(\le\) \(\dfrac{4}{7}\)
=> 1 - \(\dfrac{4}{3x^2+7}\) \(\ge\) \(\dfrac{3}{7}\)
Vậy D đạt GTNN khi bằng \(\dfrac{3}{7}\)
Dấu "=" xảy ra khi x = 0