Bài 13:
a) \(x^3-49x=0\)
\(\Leftrightarrow x\left(x^2-49\right)=0\)
\(\Leftrightarrow x\left(x+7\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+7=0\\x-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-7\\x=7\end{matrix}\right.\)
b) \(x^3-3x^2+3x-1=0\)
\(\Leftrightarrow x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3=0\)
\(\Leftrightarrow\left(x-1\right)^3=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
c) \(x^3+6x^2+9x=0\)
\(\Leftrightarrow x\left(x^2+6x+9\right)=0\)
\(\Leftrightarrow x\left(x^2+2\cdot3\cdot x+3^2\right)=0\)
\(\Leftrightarrow x\left(x+3\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
d) \(\left(x+5\right)^2-16x^2=0\)
\(\Leftrightarrow\left(x+5\right)^2-\left(4x\right)^2=0\)
\(\Leftrightarrow\left(x+5-4x\right)\left(x+5+4x\right)=0\)
\(\Leftrightarrow\left(5-3x\right)\left(5x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5-3x=0\\5x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=5\\5x=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-1\end{matrix}\right.\)
12:
a: \(4x^2+4x+1=0\)
=>\(\left(2x\right)^2+2\cdot2x\cdot1+1^2=0\)
=>\(\left(2x+1\right)^2=0\)
=>2x+1=0
=>2x=-1
=>\(x=-\dfrac{1}{2}\)
b: \(x^2-2x=-1\)
=>\(x^2-2x+1=0\)
=>\(x^2-2\cdot x\cdot1+1^2=0\)
=>\(\left(x-1\right)^2=0\)
=>x-1=0
=>x=1
c: \(-x^2+10x=25\)
=>\(-x^2+10x-25=0\)
=>\(x^2-10x+25=0\)
=>\(x^2-2\cdot x\cdot5+5^2=0\)
=>\(\left(x-5\right)^2=0\)
=>x-5=0
=>x=5
d: \(12x-4x^2=9\)
=>\(-4x^2+12x-9=0\)
=>\(4x^2-12x+9=0\)
=>\(\left(2x\right)^2-2\cdot2x\cdot3+3^2=0\)
=>\(\left(2x-3\right)^2=0\)
=>2x-3=0
=>2x=3
=>x=3/2
