Question

(2x-5)² - x² - 4x - 4 = 0  

Answer 1

\(...=0\) \(\Leftrightarrow\left(2x-5\right)^2-\left(x+2\right)^2=0\Leftrightarrow\left(x-7\right)\left(3x-3\right)=0\)  \(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)

 

Answer 2

`( 2x - 5 )^2 - x^2 - 4x - 4 = 0`

`<=> 4x^2 - 20x + 25 - x^2 - 4x - 4 = 0`

`<=> 3x^2 - 24x + 21 = 0`

`<=> 3x^3 - 3x - 21x + 21 = 0`

`<=> 3x ( x - 1 ) - 21 ( x - 1 ) = 0`

`<=> ( x - 1 ) ( 3x - 21 ) = 0`

`<=>`$\left[\begin{matrix} x-1=0\\ 3x-21=0\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=1\\ x=7\end{matrix}\right.$

Vậy `S = { 1 ; 7 }`