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a,|x2−13x2−13| = 3232
b, 32−1232−12 ( 2x-1)=3434
c, |x-1|+2x=2
a)\(\left|\dfrac{x}{2}-\dfrac{1}{3}\right|=\dfrac{3}{2}\)
TH1
\(\dfrac{x}{2}-\dfrac{1}{3}=\dfrac{3}{2}\)
=>\(\dfrac{x}{2}=\dfrac{11}{6}\)
=>x=\(\dfrac{11.2}{6}\)
=>x=\(\dfrac{11}{3}\)
TH2
\(\dfrac{x}{2}-\dfrac{1}{2}=-\dfrac{3}{2}\)
=>\(\dfrac{x}{2}=-\dfrac{3}{2}+\dfrac{1}{2}\)
=>\(\dfrac{x}{2}=-1\)
=>x=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
ĐKXĐ: \(2x\geq 0\Leftrightarrow x\geq 0\)
Vậy TXĐ của $x$ là \(D= [0;+\infty)\)
b)
ĐK: \((2x-1)(x+3)\neq 0\Leftrightarrow \left\{\begin{matrix} 2x-1\neq 0\\ x+3\neq 0\end{matrix}\right.\Leftrightarrow \Leftrightarrow \left\{\begin{matrix} x\neq \frac{1}{2}\\ x\neq -3\end{matrix}\right.\)
Vậy TXĐ \(D=\mathbb{R}\setminus \left\{\frac{1}{2}; -3\right\}\)
c)
ĐK: \(8x^3+1\neq 0\Leftrightarrow x^3\neq \frac{-1}{8}\Leftrightarrow x\neq \frac{-1}{2}\)
Vậy TXĐ \(D=\mathbb{R}\setminus \left\{\frac{-1}{2}\right\}\)
d)
ĐK:
\(|x-2015|+1\neq 0\Leftrightarrow |x-2015|\neq -1\Leftrightarrow x\in\mathbb{R}\)
Vậy TXĐ \(D=\mathbb{R}\)
e)
ĐK: \(\left\{\begin{matrix} |x-1,2|\neq 0\\ 2x-5\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq 1,2\\ x\neq 2,5\end{matrix}\right.\)
Vậy TXĐ: \(D=\mathbb{R}\setminus \left\{1,2; 2,5\right\}\)
f)
ĐK: \(x^2-4\neq 0\Leftrightarrow (x-2)(x+2)\neq 0\Leftrightarrow x\neq \pm 2\)
Vậy TXĐ: \(D=\mathbb{R}\setminus \left\{\pm 2\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)Ta có: \(x^2 - 2 = 0 \)
\(=> x^2 = 2\)
\(\Rightarrow x=\pm\sqrt{2}\)
b)Ta có : \(x^2\ge0\) \(\forall x\in R\)
\(\Rightarrow x^2+\sqrt{3}\ge\sqrt{3}\ne0\)
Vậy đa thức trên vô nghiệm
![](https://rs.olm.vn/images/avt/0.png?1311)
a/ Ta có :
\(f\left(x\right)=\left(9x^3-\frac{1}{3}x^3\right)+\left(3x^2+\frac{1}{3}x^2-3x^2\right)+\left(-\frac{1}{3}x-3x+3x\right)+\left(27-9\right)\)
\(=\frac{26}{3}x^3+\frac{1}{3}x^2-\frac{1}{3}x+18\)
Vậy...
b/ Ta có :
+) \(P\left(3\right)=\frac{26}{3}.3^3+\frac{1}{3}.3^2-\frac{1}{3}.3+18=254\)
+) \(P\left(-3\right)=\frac{26}{3}.\left(-3\right)^3+\frac{1}{3}.\left(-3\right)^2-\frac{1}{3}.\left(-3\right)+18=-212\)
Vậy..
(2x + 3)^3 = -27
=> 2x + 3 = -3
=> 2x = -6
=> x = -3
\(\left(2x+3\right)^3=-27\)
\(\left(2x+3\right)^3=\left(-3\right)^3\)
\(\Rightarrow2x+3=-3\)
\(\Leftrightarrow2x=-6\)
\(\Leftrightarrow x=-3\)