(3x+3/5).(|x|-1/4)=0 Giúp mình với!!! Cần gấp lắm !
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Ta có x4-3x3-6x2+3x+1=0
<=> (x4+x3-x2)-(43+4x2-4x)-(x2+x-1) =0
<=> (x2-4x-1)(x2+x-1) =0
=> \(^{\orbr{\begin{cases}x^2-4x-1=0\\x^2+x-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\pm\sqrt{5}\\x=\pm\frac{\sqrt{5}-1}{2}\end{cases}}}\)

\(x\left(3x-5\right)-9x+15=0\)
\(\Leftrightarrow x\left(3x-5\right)-3\left(3x-5\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(3x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\3x-5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\frac{5}{3}\end{cases}}\)
\(3x\left(x-5\right)-2\left(5-x\right)=0\)
\(\Leftrightarrow3x\left(x-5\right)+2\left(x-5\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}3x+2=0\\x-5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-2}{3}\\x=5\end{cases}}\)

\(\frac{1}{2}\times\left(x-\frac{4}{5}\right)+\frac{3}{4}x=\frac{5}{12}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{2}{5}+\frac{3}{4}x=\frac{5}{12}\)
\(\Leftrightarrow\frac{1}{2}x+\frac{3}{4}x=\frac{5}{12}+\frac{2}{5}\)
\(\Leftrightarrow\frac{5}{4}x=\frac{49}{60}\)
\(\Leftrightarrow x=\frac{49}{75}\)
Vậy \(x=\frac{49}{75}\)

\(\Leftrightarrow\left(\frac{3}{4}x-\frac{9}{16}\right)\left(\frac{1}{3}-\frac{3}{5}.\frac{1}{x}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{3}{4}x-\frac{9}{16}=0\\\frac{1}{3}-\frac{3}{5}.\frac{1}{x}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=\frac{9}{5}\end{cases}}\)
Vậy \(x\in\left\{\frac{3}{4};\frac{9}{5}\right\}\)

a) \(x+xy-y=8\)
\(\Leftrightarrow x.\left(1+y\right)-y=8\)
\(\Leftrightarrow x.\left(1+y\right)-y-1=8-1\)
\(\Leftrightarrow x.\left(1+y\right)-\left(1+y\right)=7\)
\(\Leftrightarrow\left(1+y\right).\left(x-1\right)=7\)
Lập bảng tìm tiếp
b) Ta có: \(\hept{\begin{cases}\left(x+2\right)^2\ge0\forall x\\\left(2y-6\right)^4\ge0\forall x\end{cases}}\)
\(\Rightarrow\left(x+2\right)^2+\left(2y-6\right)^4\ge0\forall x\)
Do đó \(\left(x+2\right)^2+\left(2y-6\right)^4=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(x+2\right)^2=0\\\left(2y-6\right)^4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-2\\y=3\end{cases}}}\)
Vậy ...

\(\left(x-2\right)^5-\left(x-2\right)^3=0\)
\(\Rightarrow\left(x-2\right)^3\left(\left(x-2\right)^2-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^2-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\\left(x-2\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=1\\x-2=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{1;2;3\right\}\)
⇒ ( x - 2)3 . (x - 2)2 - (x - 2)3 . 1 = 0 ⇒ ( x - 2)3 . [( x - 2)2 - 1] = 0
\(\left(3x+\dfrac{3}{5}\right)\left(\left|x\right|-\dfrac{1}{4}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x+\dfrac{3}{5}=0\\\left|x\right|=\dfrac{1}{4}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{5}\\x=\dfrac{1}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{-\dfrac{1}{5};\dfrac{1}{4};-\dfrac{1}{4}\right\}\)
⇒\(\left\{{}\begin{matrix}3x+\dfrac{3}{5}=0\\\left|x\right|-\dfrac{1}{4}=0\end{matrix}\right.\) ⇒\(\left\{{}\begin{matrix}3x=0-\dfrac{3}{5}=-\dfrac{3}{5}\\\left|x\right|=0+\dfrac{1}{4}=\dfrac{1}{4}\end{matrix}\right.\)
⇒\(\left\{{}\begin{matrix}x=-\dfrac{3}{5}:3=-\dfrac{1}{5}\\x=\dfrac{1}{4},-\dfrac{1}{4}\end{matrix}\right.\)