Đáp án:
$1.$ \(\left[ \begin{array}{l}x=78\\x=-\frac{4}{5}\end{array} \right.\)
$2.$ \(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
$3.$ \(\left[ \begin{array}{l}x=2\\x=1\end{array} \right.\)
$4. x = \frac{3}{4}$
$5.$ \(\left[ \begin{array}{l}x=1\\x=\frac{1}{5}\end{array} \right.\)
Giải thích các bước giải:
$1. 5x( x - 78 ) + 4( x - 78 ) = 0$
⇔ $( x - 78 )( 5x + 4 ) = 0$
⇔ \(\left[ \begin{array}{l}x=78\\x=-\frac{4}{5}\end{array} \right.\)
$2. ( 3x - 5 )^{2} - ( x + 1 )^{2} = 0$
⇔ $( 3x - 5 - x - 1 )( 3x - 5 + x + 1 ) = 0$
⇔ $( 2x - 6 )( 4x - 4 ) = 0$
⇔ $( x - 3 )( x - 1 ) = 0$
⇔ \(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
$3. x( x - 2 ) - x + 2 = 0$
⇔ $x( x - 2 ) - ( x - 2 ) = 0$
⇔ $( x - 2 )( x - 1 ) = 0$
⇔ \(\left[ \begin{array}{l}x=2\\x=1\end{array} \right.\)
$4. ( 10x + 9 )x - ( 5x - 1 )( 2x + 3 ) = 0$
⇔ $10x^{2} + 9x - ( 10x^{2} + 13x - 3 ) = 0$
⇔ $10x^{2} + 9x - 10x^{2} - 13x + 3 = 0$
⇔ $- 4x + 3 = 0$
⇔ $x = \frac{3}{4}$
$5. 5x( x - 1 ) = ( x - 1 )$
⇔ $5x( x - 1 ) - ( x - 1 ) = 0$
⇔ $( x - 1 )( 5x - 1 ) = 0$
⇔ \(\left[ \begin{array}{l}x=1\\x=\frac{1}{5}\end{array} \right.\)
