a) $15x^3 - 30x = 0$
⇔ $15x(x^2 - 2) = 0$
⇔ $x(x^ - 2) = 0$
⇔ \(\left[ \begin{array}{l}x=0\\x^2 = 2⇔x = \sqrt 2 = -\sqrt 2\end{array} \right.\)
b) $3(x-1000) = 5x(x-1000)$
⇔ $3(x-1000) - 5x(x-1000) = 0$
⇔ $(3 - 5x)(x-1000) = 0$
⇔ \(\left[ \begin{array}{l}3 -5x = 0 <=> x = \dfrac{3}{5}\\x-1000 = 0 <=> x = 1000\end{array} \right.\)
c) $(2 - 2x)^2 = 2 - 2x$
⇔ $(2 - 2x)^2 - (2 - 2x) = 0$
⇔ $(2 - 2x)(2 - 2x - 1) = 0$
⇔ $(2 - 2x)(1 - 2x) = 0$
⇔ \(\left[ \begin{array}{l}2-2x = 0 <=> x = 1\\1 - 2x = 0 <=> x = \dfrac{1}{2}\end{array} \right.\)
d) $(2x^2 + 1)(3x - 9) + 3x = 9$
⇔ $6x^3 - 18x^2 + 3x - 9 + 3x - 9 = 0$
⇔ $6x^3 - 18x^2 + 6x - 18 = 0$
⇔ $6x^2(x - 3) + 6(x-3) = 0$
⇔ $6(x-3)(x^2 + 1) = 0$
⇔ $(x-3)(x^2 + 1) = 0$
⇔ \(\left[ \begin{array}{l}x-3= 0 <=> x = 3\\x^2 + 1 = 0 <=> x^2 = -1 (loại)\end{array} \right.\)
e) $(5x + 20)(x^2 + 17) - 10x = 20$ (Đề lỗi)
f) $\dfrac{x^7}{8} - \dfrac{x^6}{2} = 0$
⇔ $\dfrac{x^7 - 4x^6}{8} = 0 $
⇔ $x^7 - 4x^6 = 0$
⇔ $x^6(x - 4) = 0$
⇔ \(\left[ \begin{array}{l}x^6 = 0 <=> x= 0\\x - 4 = 0 <=> x = 4\end{array} \right.\)
