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a) \(\frac{x^2-xy}{5y^2-5xy}\)=\(\frac{x\left(x-y\right)}{-5y\left(x-y\right)}\)=\(\frac{-x}{5y}\)
b) \(\frac{3x^2-12x+12}{x^4-8x}\)=\(\frac{3\left(x^2-4x+4\right)}{x\left(x^3-2^3\right)}\)=\(\frac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+2x+4\right)}\)=\(\frac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)
Ta có:
\(x^3+x^2-4x=4\)
\(\Rightarrow x^3+x^2-4x-4=0\)
\(\Rightarrow\left(x^3+x^2\right)-\left(4x+4\right)=0\)
\(\Rightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Rightarrow\left(x^2-4\right)\left(x+1\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)\left(x+1\right)=0\)
\(\Rightarrow x-2=0;x+2=0;x+1=0\)
\(\Rightarrow x\in\left\{2;-2;-1\right\}\)
a)\(2.\left(x+5\right)-x^2-5x=0\)
\(\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right).\left(2-x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+5=0\\2-x=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-5\\x=2\end{cases}}\)
b)\(3x^3-48x=0\)
\(\Leftrightarrow3x\left(x^2-16\right)=0\)
\(\Leftrightarrow3x.\left(x-4\right).\left(x+4\right)=0\)
\(\Leftrightarrow\orbr{\frac{x=4}{\frac{x=0}{x=-4}}}\)
c)\(x^3+x^2-4x=4\)
\(\Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{x=0}{x=2}\\\overline{x=-2}\end{cases}}\)
Câu hỏi của Nàng tiên cá - Toán lớp 8 - Học toán với OnlineMath
Em tham khảo nhé!
b,\(4x^2-20x=0\)
⇔\(4x\left(x-5\right)=0\)
⇔\(\left\{{}\begin{matrix}4x=0\\x-5=0\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
c,\(\left(3x-2\right)\left(4x+5\right)=0\)
⇔\(\left\{{}\begin{matrix}3x-2=0\\4x+5=0\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=\dfrac{2}{3}\\x=-1.25\end{matrix}\right.\)
e,\(\left(x^2+1\right)\left(x-2\right)=0\)
⇔\(\left\{{}\begin{matrix}x^2+1=0\\x-2=0\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x^2=-1\left(loai\right)\\x=2\left(nhan\right)\end{matrix}\right.\)
⇔\(x=2\)
a) Ta có: \(\dfrac{x-3}{2011}+\dfrac{x-2}{2012}=\dfrac{x-2012}{2}+\dfrac{x-2011}{3}\)
\(\Leftrightarrow\dfrac{x-3}{2011}+\dfrac{x-2}{2012}-\dfrac{x-2012}{2}-\dfrac{x-2011}{3}=0\)
\(\Leftrightarrow\dfrac{x-3}{2011}-1+\dfrac{x-2}{2012}-1-\dfrac{x-2012}{2}+1-\dfrac{x-2011}{3}+1=0\)
\(\Leftrightarrow\dfrac{x-2014}{2011}+\dfrac{x-2014}{2012}-\dfrac{x-2014}{2}-\dfrac{x-2014}{3}=0\)
\(\Leftrightarrow\left(x-2014\right)\left(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\)
mà \(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2}-\dfrac{1}{3}\ne0\)
nên x-2014=0
hay x=2014
Vậy: S={2014}
b) Ta có: \(4x^2-20x=0\)
\(\Leftrightarrow4x\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
Vậy: S={0;5}
c) Ta có: \(\left(3x-2\right)\left(4x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-2=0\\4x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=2\\4x=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{5}{4}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{2}{3};-\dfrac{5}{4}\right\}\)
d) Ta có: \(\dfrac{x-5}{75}+\dfrac{x-2}{78}+\dfrac{x-6}{74}+\dfrac{x-68}{12}=4\)
\(\Leftrightarrow\dfrac{x-5}{75}-1+\dfrac{x-2}{78}-1+\dfrac{x-6}{74}-1+\dfrac{x-68}{12}-1=0\)
\(\Leftrightarrow\dfrac{x-80}{75}+\dfrac{x-80}{78}+\dfrac{x-80}{74}+\dfrac{x-80}{12}=0\)
\(\Leftrightarrow\left(x-80\right)\left(\dfrac{1}{75}+\dfrac{1}{78}+\dfrac{1}{74}+\dfrac{1}{12}\right)=0\)
mà \(\dfrac{1}{75}+\dfrac{1}{78}+\dfrac{1}{74}+\dfrac{1}{12}>0\)
nên x-80=0
hay x=80
Vậy: S={80}
e) Ta có: \(\left(x^2+1\right)\left(x-2\right)=0\)
mà \(x^2+1>0\forall x\)
nên x-2=0
hay x=2
Vậy: S={2}