![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left[{}\begin{matrix}3x+\sqrt{2}=4\\3x+\sqrt{2}=-4\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}3x=4-\sqrt{2}\\3x=-4-\sqrt{2}\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}x=\dfrac{4-\sqrt{2}}{3}\\x=\dfrac{-4-\sqrt{2}}{3}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{x}=x\)
\(\Rightarrow x-\sqrt{x}=0\)
\(\Rightarrow\sqrt{x}\left(\sqrt{x}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\end{matrix}\right.\)
\(x-2\sqrt{x}=0\)
\(\Rightarrow\sqrt{x}\left(\sqrt{x}-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)
\(\sqrt{x+1}=1-x\)
\(\Rightarrow\left|x+1\right|=1-2x+x^2\)
Với \(x\ge-1\) ta có:
\(x+1=1-2x+x^2\)
\(\Rightarrow x+1-1+2x-x^2=0\)
\(\Rightarrow3x-x^2=0\)
\(\Rightarrow x\left(3-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
Với \(x< -1\) ta có:
\(-x-1=1-2x+x^2\)
\(\Rightarrow1-2x+x^2+x-1=0\)
\(\Rightarrow3x+x^2=0\)
\(\Rightarrow x\left(3+x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\3+x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
Còn pt vô tỉ tui chưa học
![](https://rs.olm.vn/images/avt/0.png?1311)
Haizz.... Toàn bài mình đăng tự năm trc xg đến năm sau mình làm .......:))
\(\sqrt{3x^2+4}+\sqrt{2004.x^2+1}=3-4x^2\) (1)
Ta xét 2 trường hợp
TH1 : x = 0
Khi đó (1) \(\Leftrightarrow\sqrt{3.0+4}+\sqrt{2004.0+1}=3-4.0\)
\(\Leftrightarrow\sqrt{0+4}+\sqrt{0+1}=3-0\)
\(\Leftrightarrow\sqrt{4}+\sqrt{1}=3\)
\(\Leftrightarrow2+1=3\) ( thỏa mãn)
\(\Rightarrow x=0\) thỏa mãn đề bài
TH2 \(x\ne0\)
Ta có \(x\ne0\Leftrightarrow x^2>0\)
\(\Leftrightarrow\hept{\begin{cases}3x^2>0\\2004x^2>0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}3x^2+4>4\\2004x^2+1>1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\sqrt{3x^2+4}>2\\\sqrt{2004x^2+1}>1\end{cases}}\)
\(\Leftrightarrow\sqrt{3x^2+4}+\sqrt{2004x^2+1}>2+1=3\) (2)
Lại có \(x^2>0\Leftrightarrow4x^2>0\)
\(\Leftrightarrow-4x^2< 0\)
\(\Leftrightarrow3-4x^2< 3\) (3)
Từ (2) và (3 ) => (1) vô lí vs mọi x khác 0
=> \(x\ne0\) loại
Vậy x = 0 thỏa mãn đề bài
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{x^4+3x^2}+\sqrt{x^4+6x^2}\)
\(=\sqrt{x^4+\dfrac{3}{2}x^2+\dfrac{3}{2}x^2+\dfrac{9}{4}-\dfrac{9}{4}}+\sqrt{x^4+3x^2+3x^2+9-9}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2}+\sqrt{\left(x^2+3\right)^2-3^2}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}-\dfrac{3}{2}\right)\left(x^2+\dfrac{3}{2}+\dfrac{3}{2}\right)}+\sqrt{\left(x^2+3-3\right)\left(x^2+3+3\right)}\)
\(=\sqrt{x^2}.\sqrt{x^2+3}+\sqrt{x^2}.\sqrt{x^2+6}\)
\(=x\left(\sqrt{x^2+3}+\sqrt{x^2+6}\right)\)
\(\sqrt{x^4+3x^2}+\sqrt{x^4+6x^2}\)
\(=\sqrt{x^4+3x^2+\dfrac{9}{4}-\dfrac{9}{4}}+\sqrt{x^4+6x^2+9-9}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}\right)^2-\dfrac{9}{4}}+\sqrt{\left(x^2+3\right)^2-9}\)
\(=\left|x^2+\dfrac{3}{2}\right|-\dfrac{3}{2}+\left|x^2+3\right|-3\)
Vì: \(\left\{{}\begin{matrix}x^2+\dfrac{3}{2}>0\\x^2+3>0\end{matrix}\right.\)
Nên: \(pt\Leftrightarrow x^2+\dfrac{3}{2}-\dfrac{3}{2}+x^2+3-3\)
\(=2x^2\)
Đừng giết em :333333333
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 2|2/3 - x| = 1/2
|2/3 - x| = 1/4
|2/3 - x| = 1/4 hoặc |2/3 - x| = -1/4
Xét 2 TH...
\(\sqrt[]{2-3x}=4\left(x\le\dfrac{2}{3}\right)\)
\(\Rightarrow2-3x=16\Rightarrow3x=-14\Rightarrow x=-\dfrac{14}{3}\)
\(\sqrt{2-3x}=4\)
\(\sqrt{\left(2-3x\right)^2}=4^2\) (ĐK: \(x\le\) \(\dfrac{2}{3}\))
\(2-3x=16\)
\(3x=2-16\)
\(3x=-14\)
\(x=-\dfrac{14}{3}\)