a ) \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left[x+2-\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x+2\right)\left[x+2-x+2\right]=0\)
\(\Leftrightarrow4\left(x+2\right)=0\)
\(\Leftrightarrow x+2=0\)
\(\Leftrightarrow x=-2\)
Vậy \(x=-2\)
b ) \(\left(2x+3\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x+3-x+1\right)\left(2x+3+x-1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{2}{3}\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-4\\x=-\dfrac{2}{3}\end{matrix}\right.\)
c ) \(x^3-8=\left(x-2\right)^2\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)^2=0\)
\(\Leftrightarrow\left(x-2\right)\left[x^2+2x+4-\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x^2+x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{23}{4}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x+\dfrac{1}{2}\right)^2=-\dfrac{23}{4}\end{matrix}\right.\) ( Vô lý )
Vậy \(x=2\)
d ) \(x^3+5x^2-4x-20=0\)
\(\Leftrightarrow x^2\left(x+5\right)-4\left(x+5\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=-5\end{matrix}\right.\)
Vậy ...
e ) \(x^3-4x^2+4x=0\)
\(\Leftrightarrow x\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow x\left(x-2\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x-2\right)^2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
Vậy ...
f ) \(x^2-25+2\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5\right)+2\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-5+2\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)
g ) Sai đề
h ) \(x^2\left(x-2\right)+7x=14\)
\(\Leftrightarrow x^2\left(x-2\right)+7x-14=0\)
\(\Leftrightarrow x^2\left(x-2\right)+7\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+7=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=-7\left(VL\right)\\x=2\end{matrix}\right.\)
Vậy \(x=2\)
