Tìm x, biết:
x-{[-x+(x+3)]-[(x+3)-(x-2)]}=0
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\(\dfrac{x}{3}-\dfrac{x^2}{4}=0\\ \Leftrightarrow x\left(\dfrac{1}{3}-\dfrac{x}{4}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\\dfrac{x}{4}=\dfrac{1}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)
\(\dfrac{x}{3}-\dfrac{x^2}{4}=0\)
\(\Leftrightarrow\dfrac{4x-3x^2}{12}=0\)
\(\Leftrightarrow-3x^2+4x=0\)
\(\Leftrightarrow-3x\left(x-\dfrac{4}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)
\(x+x+x\times1+x\times6=120\\ x\times\left(1+1+1+6\right)=120\\ x\times9=120\\ x=\dfrac{120}{9}\\ x=\dfrac{40}{3}\)
a: Ta có: \(\left(2x-1\right)^2-25=0\)
\(\Leftrightarrow\left(2x-6\right)\left(2x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Lời giải:
a.
$x(x-\frac{1}{2})< 0$
\(\Leftrightarrow \left[\begin{matrix}
\left\{\begin{matrix}
x< 0\\
x-\frac{1}{2}>0\end{matrix}\right.\\
\left\{\begin{matrix}
x>0\\
x-\frac{1}{2}< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow \left[\begin{matrix}
0> x>\frac{1}{2} (\text{vô lý})\\
0< x< \frac{1}{2}(\text{chọn})\end{matrix}\right.\)
b.
\(\frac{x-1}{x+2}< 0\Leftrightarrow \left[\begin{matrix} \left\{\begin{matrix} x-1< 0\\ x+2>0\end{matrix}\right.\\ \left\{\begin{matrix} x-1>0\\ x+2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} -2< x< 1(\text{chọn})\\ -2> x>1(\text{vô lý})\end{matrix}\right.\)
\(\left(x+3\right)^{2022}+\left(\sqrt{y-2}-1\right)^{2023}=0\) \(\left(ĐKXĐ: y\ge2\right)\)
Xét \(\left(x+3\right)^{2022}\ge0\forall x\)
\(\Rightarrow\left(\sqrt{y-2}-1\right)^{2023}\le0\)
\(\Leftrightarrow\sqrt{y-2}-1\le0\)
\(\Leftrightarrow\sqrt{y-2}\le1\)
\(\Leftrightarrow y-2\le1\)
\(\Rightarrow y\le3\)
\(\Rightarrow2\le y\le3\) mà \(y\in Z\)
\(\Rightarrow\left\{{}\begin{matrix}y=2\Leftrightarrow x=-2\\y=3\Leftrightarrow x=-3\end{matrix}\right.\)
Em không nghĩ câu này đúng. Anh giải thích hộ bạn đó với ạ.
Lời giải:
$x+(x+1)+(x+2)+....+(x+21)=231$
$\underbrace{x+x+....+x}_{22}+(1+2+3+...+21)=231$
$22x+231=231$
$22x=0$
$x=0$
<=> x-[(-x+x+3)-(x+3-x+2)]=0
<=>x-(3-5)=0
<=>x+2=0
<=>x=-2
\(x-\left\{\left[-x+\left(x+3\right)\right]-\left[\left(x-3\right)-\left(x-2\right)\right]\right\}=0\)
\(x-\left\{\left[-x+x+3\right]-\left[x-3-x+2\right]\right\}=0\)
\(x-\left\{3-\left(-1\right)\right\}=0\)
\(x-\left\{3+1\right\}=0\)
\(x-4=0\)
\(x=4\)