\(\dfrac{\left(3x-2\right)^2}{3}-\dfrac{\left(2x+1\right)^2}{3}\le x\left(x+1\right)\)
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26 tháng 6 2021
Bài 1 :
Ta có : \(\dfrac{3x+5}{2}-1\le\dfrac{x+2}{3}+x\)
\(\Leftrightarrow\dfrac{3x+5}{2}-1-\dfrac{x+2}{3}-x\le0\)
\(\Leftrightarrow\dfrac{3\left(3x+5\right)-6-2\left(x+2\right)-6x}{6}\le0\)
\(\Leftrightarrow9x+15-6-2x-4-6x\le0\)
\(\Leftrightarrow x\le-5\)
Mà \(\left\{{}\begin{matrix}x\in Z\\x>-10\end{matrix}\right.\)
Vậy \(x\in\left\{-5;-6;-7;-8;-9\right\}\)
NB
26 tháng 6 2021
b3\(\Leftrightarrow2x^2+5x-3-3x+1\le x^2+2x-3+x^2-5\\ \Leftrightarrow0.x\le-6\Leftrightarrow x\in\varnothing\)
16 tháng 2 2021
a) Ta có: \(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)
\(\Leftrightarrow\left(2x-3\right)^2-\left(2x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3-x-1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=4\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{3}{2};4\right\}\)
b) Ta có: \(x\left(2x-9\right)=3x\left(x-5\right)\)
\(\Leftrightarrow x\left(2x-9\right)-3x\left(x-5\right)=0\)
\(\Leftrightarrow x\left(2x-9\right)-x\left(3x-15\right)=0\)
\(\Leftrightarrow x\left(2x-9-3x+15\right)=0\)
\(\Leftrightarrow x\left(6-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\6-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
Vậy: S={0;6}
c) Ta có: \(3x-15=2x\left(x-5\right)\)
\(\Leftrightarrow3\left(x-5\right)-2x\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(3-2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\3-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\2x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{3}{2}\end{matrix}\right.\)
Vậy: \(S=\left\{5;\dfrac{3}{2}\right\}\)
d) Ta có: \(\dfrac{5-x}{2}=\dfrac{3x-4}{6}\)
\(\Leftrightarrow6\left(5-x\right)=2\left(3x-4\right)\)
\(\Leftrightarrow30-6x=6x-8\)
\(\Leftrightarrow30-6x-6x+8=0\)
\(\Leftrightarrow-12x+38=0\)
\(\Leftrightarrow-12x=-38\)
\(\Leftrightarrow x=\dfrac{19}{6}\)
Vậy: \(S=\left\{\dfrac{19}{6}\right\}\)
e) Ta có: \(\dfrac{3x+2}{2}-\dfrac{3x+1}{6}=2x+\dfrac{5}{3}\)
\(\Leftrightarrow\dfrac{3\left(3x+2\right)}{6}-\dfrac{3x+1}{6}=\dfrac{12x}{6}+\dfrac{10}{6}\)
\(\Leftrightarrow6x+4-3x-1=12x+10\)
\(\Leftrightarrow3x+3-12x-10=0\)
\(\Leftrightarrow-9x-7=0\)
\(\Leftrightarrow-9x=7\)
\(\Leftrightarrow x=-\dfrac{7}{9}\)
Vậy: \(S=\left\{-\dfrac{7}{9}\right\}\)
26 tháng 6 2023
1:
c: =>1/3x+2/3-x+1>x+3
=>-2/3x+5/3-x-3>0
=>-5/3x-4/3>0
=>-5x-4>0
=>x<-4/5
d: =>3/2x+5/2-1<=1/3x+2/3+x
=>3/2x+3/2<=4/3x+2/3
=>1/6x<=2/3-3/2=-5/6
=>x<=-5
2:
HP
30 tháng 1 2021
1.
ĐK: \(x\ne3;x\ne-2\)
\(\dfrac{5}{x-3}+\dfrac{3}{x+2}\le\dfrac{3+2x}{x^2-x-6}\)
\(\Leftrightarrow\dfrac{5\left(x+2\right)+3\left(x-3\right)}{x^2-x-6}\le\dfrac{3+2x}{x^2-x-6}\)
\(\Leftrightarrow\dfrac{8x+1-3-2x}{x^2-x-6}\le0\)
\(\Leftrightarrow\dfrac{6x-2}{x^2-x-6}\le0\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x-2\ge0\\x^2-x-6< 0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}6x-2\le0\\x^2-x-6>0\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}6x-2\ge0\\x^2-x-6< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{3}\\-2< x< 3\end{matrix}\right.\Leftrightarrow\dfrac{1}{3}\le x< 3\)
TH2: \(\left\{{}\begin{matrix}6x-2\le0\\x^2-x-6>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{1}{3}\\\left[{}\begin{matrix}x>3\\x< -2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow x< -2\)
Vậy ...
HP
30 tháng 1 2021
2.
ĐK: \(x\ne\pm2\)
\(\dfrac{1}{x^2-4}+\dfrac{2}{x+2}>-\dfrac{3}{x-2}\)
\(\Leftrightarrow\dfrac{1}{x^2-4}+\dfrac{2\left(x-2\right)+3\left(x+2\right)}{x^2-4}>0\)
\(\Leftrightarrow\dfrac{5x+3}{x^2-4}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}5x+3>0\\x^2-4>0\end{matrix}\right.\\\left\{{}\begin{matrix}5x+3< 0\\x^2-4< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{3}{5}< x< 2\\x< -2\end{matrix}\right.\)
Vậy ...
\(\Leftrightarrow\left(3x-2\right)^2-\left(2x+1\right)^2< =3\left(x^2+x\right)\)
\(\Leftrightarrow9x^2-12x+4-4x^2-4x-1-3x^2-3x< =0\)
\(\Leftrightarrow2x^2-19x+3< =0\)
Đặt \(2x^2-19x+3=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1=\dfrac{19+\sqrt{337}}{4}\\x_2=\dfrac{19-\sqrt{337}}{4}\end{matrix}\right.\)
=>F(x)=2x2-19x+3<=0 khi \(x\in\left[\dfrac{19-\sqrt{337}}{4};\dfrac{19+\sqrt{337}}{4}\right]\)