5x( x - 3 ) - 2x +6 =0
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\(\left(2x-1\right)^2+\left(x-3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x-1+x-3\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\3x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=1\\3x=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{4}{3}\end{matrix}\right.\)
Vậy \(S=\left\{\dfrac{1}{2};\dfrac{4}{3}\right\}\)
\(S=\sqrt{x^2-2x+1+9}=\sqrt{\left(x-1\right)^2+9}\ge\sqrt{9}=3\)
chọn B
Trl :
2x + 5x + 7x = 22.7
14x = 4.7
14x = 28
x= 28 : 14
x = 2
Hok tốt
a,\(\left(x-4-5\right)\left(x-4+5\right)=0\Leftrightarrow\left(x-9\right)\left(x+1\right)=0\Leftrightarrow x=9;x=-1\)
b, \(\left(x-3-x-1\right)\left(x-3+x+1\right)=0\Leftrightarrow2x-2=0\Leftrightarrow x=1\)
c, \(\left(x^2-4\right)\left(2x-3\right)-\left(x^2-4\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(2x-3-x+1\right)=0\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-2\right)=0\Leftrightarrow x=-2;x=2\)
d, \(\left(3x-7\right)^2-\left(2x+2\right)^2=0\Leftrightarrow\left(3x-7-2x-2\right)\left(3x-7+2x+2\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(5x-5\right)=0\Leftrightarrow x=1;x=9\)
\(4x^2+4x+1+4x+2-2x^2-x\le0\)
\(\Leftrightarrow2x^2+7x+3\le0\Leftrightarrow\left(2x+1\right)\left(x+3\right)\le0\)
TH1 : \(\left\{{}\begin{matrix}2x+1\ge0\\x+3\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{1}{2}\\x\le-3\end{matrix}\right.\)<=> -1/2 =< x =< -3
TH2 : \(\left\{{}\begin{matrix}2x+1\le0\\x+3\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le-\dfrac{1}{2}\\x\ge-3\end{matrix}\right.\)( vô lí )
\(5x^2-3=0\Leftrightarrow x^2=\dfrac{3}{5}\Leftrightarrow x=\pm\sqrt{\dfrac{3}{5}}=\pm\dfrac{\sqrt{15}}{5}\)
\(4x^3+x=0\Leftrightarrow x\left(4x^2+1\right)=0\Leftrightarrow x=0;4x^2+1>0\)
\(5x^2-3=0\\ \Leftrightarrow5x^2=3\\ \Leftrightarrow x^2=\dfrac{3}{5}\\\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{3}{5}}\\x=-\sqrt{\dfrac{3}{5}}\end{matrix}\right. \)
vậy \(x=\sqrt{\dfrac{3}{5}}\) ;\(x=-\sqrt{\dfrac{3}{5}}\)
\(4x^3+x=0\\ \Leftrightarrow x\left(4x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\4x^2+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\4x^2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=\dfrac{-1}{4}\left(vl\right)\end{matrix}\right.\)
vậy x=0
Câu 1:
a) 2(x-3)-3(x-5)=4(3-x)-18
<=> 3x-6-3x+15-12+4x+18=0
<=> 4x+15=0
<=> 4x=-15
<=> x=-15/4
b) -2(2x-8)+3(4-2x)=-57-5(3x-7)
<=> -4x+16+12-6x+57+15x-35=0
<=> -5x+50=0
<=> -5x=-50
<=> x=10
c) 3|2x2-7|=33
<=> |2x2-7|=11
<=> \(\orbr{\begin{cases}2x^2-7=11\\2x^2-7=-11\end{cases}\Leftrightarrow\orbr{\begin{cases}2x^2=18\\2x^2=-4\end{cases}\Leftrightarrow}\orbr{\begin{cases}x^2=9\\x^2=-2\end{cases}\Leftrightarrow}x=\pm3}\)
d) có 9x+17=3(3x+2)+11
=> 11 chia hết cho 3x+2
=> 3x+2 thuộc Ư (11)={-11;-1;1;11}
ta có bảng
3x+2 | -11 | -1 | 1 | 11 |
x | -13/3 | -1 | -1/3 | 3 |
Câu 2:
xy-5x+y=17
<=> x(y-5)+(y-5)=12
<=> (y-5)(x+5)=12
=> y-5; x+5 \(\inƯ\left(12\right)=\left\{-12;-6;-4;-3;-2;-1;1;2;3;4;6;12\right\}\)
lập bảng tương tự câu 1
\( \left(5x-2\right)\left(x-3\right)=0\)
\(\left[{}\begin{matrix}5x-2=0\\x-3=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=3\end{matrix}\right.\)
dạ em cảm ơn ạ