Đáp án:
1. \(\left[ \begin{array}{l}x=\\x=±3\end{array} \right.\)
2. $x = 2$
3. \(\left[ \begin{array}{l}x=-1\\x=\frac{2}{7}\end{array} \right.\)
4. \(\left[ \begin{array}{l}x=4\\x=5\end{array} \right.\)
5. \(\left[ \begin{array}{l}x=\frac{1}{7}\\x=0\end{array} \right.\)
6. $x = 0$
Giải thích các bước giải:
1. $4x^{3} = 36x$
⇔ $4x( x^{2} - 9 ) = 0$
⇔ \(\left[ \begin{array}{l}x=0\\x^{2}=9\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\\x=±3\end{array} \right.\)
2. $x^{3} - 6x^{2} + 12x - 8 = 0$
⇔ $x^{2}( x - 2 ) - 4x( x - 2 ) + 4( x - 2 ) = 0$
⇔ $( x - 2 )( x^{2} - 4x + 4 ) = 0$
⇔ $( x - 2 )( x - 2 )^{2} = 0$
⇔ $( x - 2 )^{3} = 0$
⇔ $x = 2$
3. $( 5x - 4 )^{2} - 81x^{2} = 0$
⇔ $( 5x - 4 )^{2} = 81x^{2}$
⇔ \(\left[ \begin{array}{l}5x-4=9x\\5x-4=-9x\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-1\\x=\frac{2}{7}\end{array} \right.\)
4. $( x - 4 )^{2} - ( x - 4 ) = 0$
⇔ $( x - 4 )( x - 4 - 1 ) = 0$
⇔ $( x - 4 )( x - 5 ) = 0$
⇔ \(\left[ \begin{array}{l}x=4\\x=5\end{array} \right.\)
5. $1 - 7x - ( 7x - 1 )^{2} = 0$
⇔ $( 7x - 1 )( -1 - 7x + 1 ) = 0$
⇔ $( 7x - 1 )( -7x ) = 0$
⇔ \(\left[ \begin{array}{l}x=\frac{1}{7}\\x=0\end{array} \right.\)
6. $( 2x - 5 )^{2} - ( 5 + 2x )^{2} = 0$
⇔ $( 2x - 5 )^{2} = ( 2x + 5 )^{2}$
⇔ \(\left[ \begin{array}{l}2x-5=2x+5\\2x-5=-2x-5\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}0x=10 ( vô lí )\\x=0\end{array} \right.\)
⇔ $x = 0$
