2x - | x + 1 | = -1/2
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\(x(x-1)(x+1)-(x-3)(x^2+2x+9)\)
\(=x\left(x^2-1\right)-\left[x\left(x^2+2x+9\right)-3\left(x^2+2x+9\right)\right]\)
\(=x^3-x-\left(x^3+2x^2+9x-3x^2-6x-27\right)\)
\(=x^3-x-\left(x^3-x^2+3x-27\right)\)
\(=x^3-x-x^3+x^2-3x+27\)
\(=x^2-4x+27\)
#\(Toru\)
$D\,=2x(10x^2-5x-2)-5x(4x^2-2x-1)\\\quad =20x^3-10x^2-4x-20x^3+10x^2+5x\\\quad =(20x^3-20x^3)+(-10x^2+10x^2)+(-4x+5x)\\\quad =x$
Thay $x=-5$ vào $D=x$
$\Rightarrow D=-5$
Vậy $D=-5$ với $x=-5$
Ta có: \(D=2x\left(10x^2-5x-2\right)-5x\left(4x^2-2x-1\right)\)
\(=20x^3-10x^2-4x-20x^2+10x^2+5x\)
=x=-5
9x2 - 4 = (2x - 1)(3x + 2)
=> (3x - 2)(3x + 2) - (2x - 1)(3x + 2) = 0
=> (3x + 2)(3x - 2 - 2x + 1) = 0
=> (3x + 2)(x - 1) = 0
=> \(\orbr{\begin{cases}3x+2=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{2}{3}\\x=1\end{cases}}\)
\(TH1:\left|x+1\right|=x+1\\ \Leftrightarrow2x-\left(x+1\right)=-\dfrac{1}{2}\\ \Leftrightarrow2x-x-1=-\dfrac{1}{2}\\ \Leftrightarrow x-1=-\dfrac{1}{2}\\ \Leftrightarrow x=-\dfrac{1}{2}+1\\ \Leftrightarrow x=\dfrac{1}{2}\\ TH2:\left|x+1\right|=-x-1\\ \Leftrightarrow2x-\left(-x-1\right)=-\dfrac{1}{2}\\ \Leftrightarrow2x+x+1=-\dfrac{1}{2}\\ \Leftrightarrow3x=-\dfrac{1}{2}-1\\ \Leftrightarrow3x=-\dfrac{3}{2}\\ \Leftrightarrow x=\left(-\dfrac{3}{2}\right):3=-\dfrac{1}{2}\)
Thay lần lượt \(x=\dfrac{1}{2};x=-\dfrac{1}{2}\) vào pt
\(\Rightarrow x=\dfrac{1}{2}\left(thoaman\right)\)
Vậy \(x=\dfrac{1}{2}\)
\(2x-\left|x+1\right|=-\dfrac{1}{2}\)
\(\left|x+1\right|=2x+\dfrac{1}{2}\)
\(\left[{}\begin{matrix}x+1=2x+\dfrac{1}{2}\\x+1=-2x-\dfrac{1}{2}\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy \(x\in\left\{\dfrac{1}{2};-\dfrac{1}{2}\right\}\).