a ) \(x^3-x=0\)
\(\Leftrightarrow x\left(x^2-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
Vậy..................
b ) \(x^3+5x^2+4x+20=0\)
\(\Leftrightarrow x^2\left(x+5\right)+4\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x^2+4\right)=0\)
\(\Leftrightarrow\left(x+5\right)=0\) . Vì \(x^2+4>0\)
\(\Leftrightarrow x=-5\)
c) \(x^2-25+3\left(x-5\right)^2=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5\right)+3\left(x-5\right)^2=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5+3x-15\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(4x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\4x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{10}{4}\end{matrix}\right.\)
Vậy......................
d ) Có nhầm đề không ?
Giải:
a) \(x^3-x=0\)
\(\Leftrightarrow x\left(x^2-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
Vậy ...
b) \(x^3+5x^2+4x+20=0\)
\(\Leftrightarrow x^2\left(x+5\right)+4\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x^2+4\right)=0\)
\(\Leftrightarrow x+5=0\left(x^2+4>0\right)\)
\(\Leftrightarrow x=-5\)
Vậy ...
c) \(x^2-25+3\left(x-5\right)^2=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5\right)+3\left(x-5\right)^2=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5+3x-15\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(4x-10\right)=0\)
\(\Leftrightarrow2\left(x-5\right)\left(2x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\2x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{5}{2}\end{matrix}\right.\)
Vậy ...
d) \(2+4\sqrt{2}x+4x^2=0\)
\(\Leftrightarrow\left(\sqrt{2}\right)^2+2\sqrt{2}.2x+\left(2x\right)^2=0\)
\(\Leftrightarrow\left(\sqrt{2}+2x\right)^2=0\)
\(\Leftrightarrow\sqrt{2}+2x=0\)
\(\Leftrightarrow x=-\dfrac{\sqrt{2}}{2}\)
Vậy ...
\(a.x^3-x=0\) \(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
\(b.x^3+5x^2+4x+20=0\)
\(\Leftrightarrow x^2\left(x+5\right)+4\left(x+5\right)=0\)
\(\Leftrightarrow\left(x^2+4\right)\left(x+5\right)=0\)
Do : \(x^2+4>0\forall x\)
\(\Leftrightarrow x=-5\)
\(c.x^2-25+3\left(x-5\right)^2=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5+3x-15\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(4x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{10}{4}\end{matrix}\right.\)
Tương tự vs con còn lại.
