a) ( x + 3 )( x - 3 ) = 16
\(\Leftrightarrow x^2-9=16\)
\(\Leftrightarrow x^2-9-16=0\)
\(\Leftrightarrow x^2-25=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-5=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=5\end{matrix}\right.\)
Vậy: \(x=-5;5\)
b) x2 - 9x + 20 = 0
\(\Leftrightarrow x^2-4x-5x+20=0\)
\(\Leftrightarrow x\left(x-4\right)-5\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-5=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
Vậy: \(x=4;5\)
c) 2/x2+2x+1 - 5/x2-2x+1 = 3/1-x2
\(\Leftrightarrow\dfrac{2}{\left(x+1\right)^2}-\dfrac{5}{\left(x-1\right)^2}=-\dfrac{3}{x^2-1}\)
\(\Leftrightarrow\dfrac{2}{\left(x+1\right)^2}-\dfrac{5}{\left(x-1\right)^2}=-\dfrac{3}{\left(x-1\right)\left(x+1\right)}\)
\(ĐKXĐ:xe\pm1\)
\(\Rightarrow2\left(x-1\right)^2-5\left(x+1\right)^2=-3\left(x^2-1\right)\)
d) | x + 4 | = 2x + 1
\(\Leftrightarrow\left[{}\begin{matrix}x+4=2x+1\\-\left(x+4\right)=2x+1\end{matrix}\right.\)khi \(\begin{matrix}x\ge4\\x< 4\end{matrix}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2x=1-4\\-x-2x=1-\left(-4\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}-x=-3\\-3x=5\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(KTM\right)\\x=\dfrac{5}{3}\left(TM\right)\end{matrix}\right.\)
Vậy: \(x=\dfrac{5}{3}\)
