a) \(\left(x-4\right)^2-25=0\)
=> (x-4)2 = 25
Suy ra \(\left\{\begin{matrix}x-4=5\\x-4=-5\end{matrix}\right.\)
=> \(\left\{\begin{matrix}x=5+4\\x=-5+4\end{matrix}\right.\)
=>\(\left\{\begin{matrix}x=9\\x=-1\end{matrix}\right.\)
2. (2x-1)2 + (2-x)(2x-1)=0
\(\Rightarrow\left(2x-1\right)\left(2x-1+2-x\right)=0\)
\(\Rightarrow\left(2x-1\right)\left(x+1\right)=0\)
\(\Rightarrow\left\{\begin{matrix}2x-1=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=\frac{1}{2}\\x=-1\end{matrix}\right.\)
3. x2+6x+9=4x2
3x2-6x-9 =0
3(x2 - 2x -3) =0
\(3\left(x^2-3x+x-3\right)=0\)
(x-3)(x+1) =0
\(\left\{\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\)
\(\left\{\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
4. (2x-5)(x+11)=(5-2x)(2x+1)
(2x-5)(x+11) + (2x-5)(2x+1)=0
(2x-5)(3x+12) =0
\(\left\{\begin{matrix}2x-5=0\\3\left(x+4\right)=0\end{matrix}\right.\)
\(\left\{\begin{matrix}x=2,5\\x=-4\end{matrix}\right.\)
5. 2x2+5x+3=0
(2x2+2x)+(3x+3)=0
2x(x+1) +3(x+1) =0
(x+1)(2x+3) =0
\(\left\{\begin{matrix}x+1=0\\2x+3=0\end{matrix}\right.\)
\(\left\{\begin{matrix}x=-1\\x=\frac{-3}{2}\end{matrix}\right.\)