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\(1,4x\left(1-x\right)-8=1-\left(4x^2+3\right)\\ \Leftrightarrow4x-4x^2-8=1-4x^2-3\\ \Leftrightarrow4x-4x^2-8-1+4x^2+3=0\\ \Leftrightarrow4x-6=0\\ \Leftrightarrow x=\dfrac{3}{2}\)
\(2,\left(2-3x\right)\left(x+11\right)=\left(3x-2\right)\left(2-5x\right)\\ \Leftrightarrow\left(2-3x\right)\left(x+11\right)-\left(2-3x\right)\left(5x-2\right)=0\\ \Leftrightarrow\left(2-3x\right)\left(x+11-5x+2\right)=0\\ \Leftrightarrow\left(2-3x\right)\left(-4x+13\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{13}{4}\end{matrix}\right.\)
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Ta có: x=2
nên x-1=1
Ta có: \(B=\left(x+1\right)\left(x^7-x^6+x^5-x^4+x^3-x^2+x-1\right)\)
\(=\left(x+1\right)\left[x^6\left(x-1\right)+x^4\left(x-1\right)+x^2\left(x-1\right)+\left(x-1\right)\right]\)
\(=\left(x+1\right)\left(x^6+x^4+x^2+1\right)\)
\(=\left(x+1\right)\left(x+1\right)\left(x^4+1\right)\)
\(=\left(2^4+1\right)\left(2+1\right)^2=17\cdot9=153\)
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\(pt\text{⇔}\left(x^2+3x+2\right)\left(x+5\right)-x^3-8x^2-27=0\text{⇔}x^3+5x^2+3x^2+15x+2x+10-x^3-8x^2-27=0\\ \text{⇔}17x=17\text{⇔}x=1\)
Vậy nghiệm của phương trình : \(S=\left\{1\right\}\)
Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+5\right)-x^3-8x^2=27\)
\(\Leftrightarrow\left(x^2+3x+2\right)\left(x+5\right)-x^3-8x^2=27\)
\(\Leftrightarrow x^3+5x^2+3x^2+15x+2x+10-x^3-8x^2=27\)
\(\Leftrightarrow17x=17\)
hay x=1
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(\dfrac{3x+2}{4}-\dfrac{3x+1}{3}=\dfrac{5}{6}\)
=>3(3x+2)-4(3x+1)=10
=>9x+6-12x-4=10
=>-3x+2=10
=>-3x=8
=>x=-8/3
b: \(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{9x-10}{4-x^2}\)
=>(x-1)(x-2)-x(x+2)=-9x+10
=>x^2-3x+2-x^2-2x=-9x+10
=>-5x+2=-9x+10
=>x=2(loại)
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\(-4\left(x-1\right)^2+\left(2x-1\right)\left(2x+1\right)=-3\) \(3\)
<=> \(-4\left(x^2-2x+1\right)+4x^2-1=-3\)
<=> \(-4x^2+8x-4+4x^2-1=-3\)
<=> \(8x-5=-3\)
<=> \(8x=2\)
<=> \(x=\frac{1}{4}\)
\(\left(\dfrac{1}{x-1}+\dfrac{1}{x+1}\right)\cdot\left(x-\dfrac{1}{x}\right)\) (1)
ĐK: \(\left\{{}\begin{matrix}x-1\ne0\\x+1\ne0\\x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\\x\ne0\end{matrix}\right.\) \(\Leftrightarrow x\ne\pm1;x\ne0\)
\(\left(1\right)=\left(\dfrac{1}{x-1}+\dfrac{1}{x+1}\right)\cdot\left(\dfrac{x^2}{x}-\dfrac{1}{x}\right)\)
\(=\left(\dfrac{1}{x-1}+\dfrac{1}{x+1}\right)\cdot\dfrac{x^2-1}{x}\)
\(=\left(\dfrac{1}{x-1}+\dfrac{1}{x+1}\right)\cdot\dfrac{\left(x+1\right)\left(x-1\right)}{x}\)
\(=\dfrac{\left(x+1\right)\left(x-1\right)}{x}\cdot\dfrac{1}{x-1}+\dfrac{\left(x+1\right)\left(x-1\right)}{x}\cdot\dfrac{1}{x+1}\)
\(=\dfrac{x+1}{x}+\dfrac{x-1}{x}\)
\(=\dfrac{x+1+x-1}{x}\)
\(=\dfrac{2x}{x}\)
\(=2\)