tim x biet x^3-3x=0
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Tim x biết:(-35-67).(3x +27)=0
-280179.(3x+27)=0
3x+27=0
3x=27
x=9
Vậy x=9
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a)Từ \(x\cdot2y=\dfrac{2x}{y}\Rightarrow2x=x\cdot2y^2\)
Do \(x,y\ne 0\) nên \(2=2y^2\Rightarrow y^2=1\Rightarrow y=\pm1\)
*)Xét \(y=1\Rightarrow3x-2=2x\Rightarrow x=2\)
*)Xét \(y=-1\Rightarrow3x+2=-2x\Rightarrow x=-\dfrac{2}{5}\)
b)\(\left|4x-3\right|+\left|3xy-5\right|=0\)
Dễ thấy: \(\left\{{}\begin{matrix}\left|4x-3\right|\ge0\\\left|3xy-5\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left|4x-3\right|+\left|3xy-5\right|\ge0\)
Xảy ra khi \(\left\{{}\begin{matrix}\left|4x-3\right|=0\\\left|3xy-5\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}4x-3=0\\3xy-5=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{4}\\3xy-5=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{4}\\y=\dfrac{20}{9}\end{matrix}\right.\)
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\(x^4-2x^3-2x^2+3x+2=0\)
\(\Leftrightarrow x^4-2x^3-2x^2+4x-x+2=0\)
\(\Leftrightarrow\left(x^4-2x^3\right)-\left(2x^2-4x\right)-\left(x-2\right)=0\)
\(\Leftrightarrow x^3\left(x-2\right)-2x\left(x-2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-2x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-x-x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left[\left(x^3-x\right)-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left[x\left(x^2-1\right)-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left[x\left(x-1\right)\left(x+1\right)-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left[\left(x^2-x\right)\left(x+1\right)-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)\left(x^2-x-1\right)=0\)
Đến đây ez r
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3-3x=0\\ \Leftrightarrow x\left(x^2-3\right)=0\\ \orbr{\begin{cases}x=0\\x^2-3=0\end{cases}}\\ \orbr{\begin{cases}x=0\\x^2=3\end{cases}}\\ \orbr{\begin{cases}x=0\\x=+_-\sqrt{3}\end{cases}}\)
x3 - 3x = 0
x.x2 - 3x = 0
x.(x2 - 3) = 0
=> x = 0 hoặc x2 - 3 = 0
=> x = 0 hoặc x2 = 3
=> x = 0 hoặc x = \(\sqrt{3}\)