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25 tháng 10 2021
\(a,\Leftrightarrow\left(4x-8\right)\left(x+1\right)=0\\ \Leftrightarrow4\left(x-2\right)\left(x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ b,\Leftrightarrow\left(x+1\right)\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2=-1\left(vô.lí\right)\end{matrix}\right.\Leftrightarrow x=-1\\ c,\Leftrightarrow x^2-2x-4x+8=0\\ \Leftrightarrow\left(x-2\right)\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\\ d,\Leftrightarrow x^3-3x^2+3x-9x+2x-6=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+x+2x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=-2\end{matrix}\right.\)
25 tháng 10 2021
a) \(\Rightarrow4\left(x+1\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
b) \(\Rightarrow x^2\left(x+1\right)+\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x^2+1\right)=0\)
\(\Rightarrow x=-1\left(do.x^2+1\ge1>0\right)\)
c) \(\Rightarrow x\left(x-4\right)-2\left(x-4\right)=0\)
\(\Rightarrow\left(x-4\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)
d) \(\Rightarrow x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)
\(\Rightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\)
\(\Rightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=-1\end{matrix}\right.\)
5 tháng 1 2022
a: \(\Leftrightarrow8x^2+16x+14x+7=0\)
=>(2x+1)(8x+7)=0
=>x=-1/2 hoặc x=-7/8
b: \(=x^3-x-6x-6\)
\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)=\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
5 tháng 1 2022
\(a,\Rightarrow8x^2+2x+28x+7=0\\ \Rightarrow2x\left(4x+1\right)+7\left(4x+1\right)=0\\ \Rightarrow\left(2x+7\right)\left(4x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{7}{2}\\x=-\dfrac{1}{4}\end{matrix}\right.\\ b,Sửa:x^3-7x-6=0\\ \Rightarrow x^3-x-6x-6=0\\ \Rightarrow x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)=0\\ \Rightarrow\left(x+1\right)\left(x^2-x-6\right)=0\\ \Rightarrow\left(x+1\right)\left(x^2-3x+2x-6\right)=0\\ \Rightarrow\left(x+1\right)\left(x-3\right)\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=3\\x=-2\end{matrix}\right.\)
26 tháng 10 2021
a: \(\Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{1}{5}\end{matrix}\right.\)
b: \(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
NT
3
M
20 tháng 11 2017
\(\left(3x-7x+3-2x\right):\left(x-3\right)=\left(3x-2x-7x+3\right):\left(x-3\right)\)
\(\left(3-6x\right):\left(x-3\right)-\left(3-6x\right):\left(x-3\right)=0\)
\(0=0\)
vậy \(x\in\varnothing\)
8 tháng 8 2021
Ta có: \(x^3-7x-6=0\)
\(\Leftrightarrow x^3-x-6x-6=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x-6\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=3\\x=-2\end{matrix}\right.\)
8 tháng 8 2021
\(x^3-7x-6=0\)
\(\Leftrightarrow x^3-x-6x-6=0\)
\(\Leftrightarrow x\left(x^2-1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[x\left(x-1\right)-6\right]=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+2x-3x-6\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-2\\x=3\end{matrix}\right.\)
Vậy...
C
1
7 tháng 9 2021
a: Ta có: \(\left(3x-2\right)\left(2x-1\right)-\left(6x^2-3x\right)=0\)
\(\Leftrightarrow2x-1=0\)
hay \(x=\dfrac{1}{2}\)
b: Ta có: \(x^3-\left(x+1\right)\left(x^2-x+1\right)=x\)
\(\Leftrightarrow x^3-x^3-1=x\)
hay x=-1
c: Ta có: \(56x^4+7x=0\)
\(\Leftrightarrow7x\left(8x^3+1\right)=0\)
\(\Leftrightarrow x\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\)
d: Ta có: \(x^2-5x-24=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-3\end{matrix}\right.\)
H
20 tháng 6 2023
\(1,=3x^2-6x+x-2=3x^2-5x-2\\ 2,??\\ 3,=3x^3y^2:3xy+6x^2y^3:3xy-12xy^4:3xy=x^2y+2xy^2-4y^3\\ 4,=3x^3y^2:4xy+6x^2y^3:4xy-12xy^4:4xy\\ =\dfrac{3}{4}x^2y+\dfrac{3}{2}xy^2-3x^3\\ 5,\left(2x^3-5x^2+7x-6\right):\left(2x-3\right)=x^2-x+2\\ 6,\left(x^4-x^3+3x^2+x+2\right):\left(x^2-1\right)=x^2-x+4\left(dư6\right)\)
20 tháng 6 2023
1: =3x^2+x-6x-2=3x^2-5x-2
3: =x^2y+2xy^2-4y^3
4: =3/4x^2y+3/2xy^2-3y^3
5: \(=\dfrac{2x^3-3x^2-2x^2+3x+4x-6}{2x-3}=x^2-x+2\)
x^3 - 4x - 3x - 6 =0
\(\Leftrightarrow\)x(x^2-4) - 3(x+2) =0
\(\Leftrightarrow\)x(x-2)(x+2) - 3(x+2)=0
\(\Leftrightarrow\)(x+2)(x^2-2x-3)=0
\(\Leftrightarrow\)(x+2)(x^2-3x+x-3)=0
\(\Leftrightarrow\)(x+2)(x+1)(x-3)=0
\(\Leftrightarrow\)x=3 hoặc x=-1 hoặc x=-3
Gọi \(A\) = \(x^3-7x-6\)
\(A=x^3-x^2+x^2-x-6x+6\)
\(A=x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)\)
\(A=\left(x-1\right)\left(x^2+x-6\right)\)
\(A=\left(x-1\right)\left(x^2+3x-2x-6\right)\)
\(A=\left(x-1\right)\left[x\left(x+3\right)-2\left(x+3\right)\right]\)
\(A=\left(x-1\right)\left(x+3\right)\left(x-2\right)\)