\(\frac{1}{9}\) .27x=3x
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a, \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
b, \(1-9x+27x^2-27x^3=-\left(3x-1\right)^3\)
Mình có làm ở câu dưới rồi . Bạn tham khảo link :
https://olm.vn/hoi-dap/detail/231817932107.html
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\(\left(27x^3+1\right):\left(9x^2-3x+1\right)=\left(3x+1\right)\left(9x^2-3x+1\right):\left(9x^2-3x+1\right)=3x+1\)
\(\left(x^3+3x^2+3x+1\right):\left(x+1\right)=\left(x+1\right)^3:\left(x+1\right)=\left(x+1\right)^2\)
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\(x^2-6x+9=\left(x-3\right)^2\)
\(4x^2+4x+1=\left(2x+1\right)^2\)
\(x^3+6x^2+12x+8=x^3+3.x^2.2+3.x.2^2+2^3=\left(x+2\right)^3\)
\(27x^3-27x^2+9x-1=\left(3x-1\right)^3\)( sửa đề chút )
\(\left(3x+2\right)\left(9x^2-6x+4\right)=\left(3x\right)^3+2^3\)( sửa đề chút )
Tham khảo nhé~
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1: \(\dfrac{x^3-11x^2+27x-9}{x-3}\)
\(=\dfrac{x^3-3x^2-8x^2+24x+3x-9}{x-3}\)
\(=x^2-8x+3\)
2: \(\dfrac{-3x^3+5x^2-9x+15}{-3x+5}\)
\(=\dfrac{3x^3-5x^2+9x-15}{3x-5}\)
\(=x^2+3\)
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1.
\(\frac{x^2+2x+5}{x+4}-\left(x-3\right)\ge0\)
\(\Leftrightarrow\frac{x^2+2x+5-\left(x-3\right)\left(x+4\right)}{x+4}\ge0\)
\(\Leftrightarrow\frac{x+17}{x+4}\ge0\Rightarrow\left[{}\begin{matrix}x>-4\\x\le-12\end{matrix}\right.\)
2.
\(\frac{x^2-3x-1}{2-x}+x>0\)
\(\Leftrightarrow\frac{x^2-3x-1+x\left(2-x\right)}{2-x}>0\)
\(\Leftrightarrow\frac{-x-1}{2-x}>0\Rightarrow\left[{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\)
3.
\(\frac{3x-47}{3x-1}-\frac{4x-47}{2x-1}>0\)
\(\Leftrightarrow\frac{\left(3x-47\right)\left(2x-1\right)-\left(4x-47\right)\left(3x-1\right)}{\left(3x-1\right)\left(2x-1\right)}>0\)
\(\Leftrightarrow\frac{-6x\left(x-8\right)}{\left(3x-1\right)\left(2x-1\right)}>0\Rightarrow\left[{}\begin{matrix}0< x< \frac{1}{3}\\\frac{1}{2}< x< 8\end{matrix}\right.\)
4.
\(\frac{x\left(x+2\right)+9}{x+2}-4\ge0\)
\(\Leftrightarrow\frac{x^2+2x+9-4\left(x+2\right)}{x+2}\ge0\)
\(\Leftrightarrow\frac{x^2-2x+1}{x+2}\ge0\)
\(\Leftrightarrow\frac{\left(x-1\right)^2}{x+2}\ge0\Rightarrow x>-2\)
5.
\(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x+6\right)}{\left(x-7\right)^3\left(x-2\right)^2}\le0\Rightarrow\left[{}\begin{matrix}x\le-6\\1\le x< 2\\2< x< 7\\x=-2\end{matrix}\right.\)
6. Xem lại đề
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<=> \(\frac{1}{9}\). (9.3)x =3x
<=> \(\frac{1}{9}\). 9x.3x = 3x
<=> \(\frac{1}{9}\). 9x = 1
<=> 9x = 9 <=> x = 1