Đáp án:
a) $S=\{-11;-2\}$
b) $S=\left\{-\dfrac{5}{2};0;\dfrac{5}{2}\right\}$
Giải thích các bước giải:
a) $9(x+5)^2-(x-7)^2=0$
$⇔(3x+15)^2-(x-7)^2=0$
$⇔(3x+15-x+7)(3x+15+x-7)=0$
$⇔(2x+22)(4x+8)=0$
$⇔(x+11)(x+2)=0$
$⇔\left[ \begin{array}{l}x+11=0\\x+2=0\end{array} \right.⇔\left[ \begin{array}{l}x=-11\\x=-2\end{array} \right.$
Vậy $S=\{-11;-2\}$
b) $8x^3-50x=0$
$⇔2x(4x^2-25)=0$
$⇔2x(2x-5)(2x+5)=0$
$⇔\left[ \begin{array}{l}2x=0\\2x-5=0\\2x+5=0\end{array} \right.⇔\left[ \begin{array}{l}x=0\\x=\dfrac{5}{2}\\x=-\dfrac{5}{2}\end{array} \right.$
Vậy $S=\left\{-\dfrac{5}{2};0;\dfrac{5}{2}\right\}$.
