(x3 - 125 ) . (x2 + x ) = 0
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( \(\dfrac{1}{125}\) - \(x^3\) ) ( \(x^2\) + 22.66) = 0
\(\left[{}\begin{matrix}\dfrac{1}{125}-x^3=0\\x^2-2^2.6^6=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x^3=\dfrac{1}{125}\\x^2=2^2(6^3)^2\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=\dfrac{1}{5}\\x^2=(2.6^3)^2\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=432^2\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=432\\x=-432\end{matrix}\right.\)
\(x\) ϵ { -432; \(\dfrac{1}{5}\); 432; }
a) x = -1. b) x = 4 hoặc x = 5.
c) x = ± 2 . d) x = 1 hoặc x = 2.
a: \(\Leftrightarrow x\left(x-5\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
\(a,\Leftrightarrow\left(4x-8\right)\left(x+1\right)=0\\ \Leftrightarrow4\left(x-2\right)\left(x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ b,\Leftrightarrow\left(x+1\right)\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2=-1\left(vô.lí\right)\end{matrix}\right.\Leftrightarrow x=-1\\ c,\Leftrightarrow x^2-2x-4x+8=0\\ \Leftrightarrow\left(x-2\right)\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\\ d,\Leftrightarrow x^3-3x^2+3x-9x+2x-6=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x^2+x+2x+2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=-2\end{matrix}\right.\)
a) \(\Rightarrow4\left(x+1\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
b) \(\Rightarrow x^2\left(x+1\right)+\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x^2+1\right)=0\)
\(\Rightarrow x=-1\left(do.x^2+1\ge1>0\right)\)
c) \(\Rightarrow x\left(x-4\right)-2\left(x-4\right)=0\)
\(\Rightarrow\left(x-4\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)
d) \(\Rightarrow x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)
\(\Rightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\)
\(\Rightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=-1\end{matrix}\right.\)
\(x^3\) + 125 + (\(x\) + 5)(\(x\) - 25) = 0
(\(x^3\) + 53) + (\(x\) + 5)(\(x\) - 25) = 0
(\(x\) + 5)(\(x^2\) - 5\(x\) + 25) + (\(x\) + 5)(\(x\) - 25) =0
(\(x\) + 5)(\(x^2\) - 5\(x\) + 25 + \(x\) - 25) = 0
(\(x\) + 5)(\(x^2\) - 4\(x\)) = 0
\(x\)(\(x\) + 5)(\(x\) - 4) = 0
\(\left[{}\begin{matrix}x=0\\x+5=0\\x-4=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=0\\x=-5\\x=4\end{matrix}\right.\)
\(\left(x^3-125\right)\left(x^2+x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^3-125=0\\x^2+x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x^3=125\\x\left(x+1\right)=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=5\\x=\left\{0;-1\right\}\end{cases}}\)
Vậy....
\(\left(x^3-125\right)\left(x^2+x\right)=0\)
=> \(\orbr{\begin{cases}x^3-125=0\\x\left(x+1\right)=0\end{cases}}\)
=> x3 = 125
hoặc x = 0
hoặc x + 1 = 0
=> x = 5
hoặc x = 1
hoặc x = -1