a) -3x² + 6x = 0
⇔ -3x.(x - 2) = 0
⇔ \(\left[ \begin{array}{l}-3x = 0\\x - 2 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 0\\x = 2\end{array} \right.\)
Vậy x ∈ {0; 2}
b) x² + 8x - x - 8 = 0
⇔ x.(x + 8) - (x + 8) = 0
⇔ (x + 8)(x - 1) = 0
⇔ \(\left[ \begin{array}{l}x + 8 = 0\\x - 1 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = -8\\x = 1\end{array} \right.\)
Vậy x ∈ {-8; 1}
c) 3x² - 48 = 0
⇔ 3x² = 48
⇔ x² = 16
⇔ x² = (± 4)²
⇒ x = ± 4
Vậy x ∈ {± 4}
d) (x + 3)² - 4 = 0
⇔ (x + 3)² = 4
⇔ (x + 3)² = (±2)²
⇒ x + 3 = ± 2
⇔ \(\left[ \begin{array}{l}x + 3 = 2\\x + 3 = -2\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = -1\\x = -5\end{array} \right.\)
Vậy x ∈ {-1; -5}
e) (x - 8)² = 36
⇔ (x - 8)² = (± 6)²
⇒ x - 8 = ± 6
⇔ \(\left[ \begin{array}{l}x - 8 = 6\\x - 8 = -6\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 14\\x = 2\end{array} \right.\)
Vậy x ∈ {14; 2}
f) x³ + 3x = 0
⇔ x.(x² + 3) = 0
⇔ \(\left[ \begin{array}{l}x = 0\\x² + 3 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 0\\x ∈ ∅\end{array} \right.\)
Vậy x = 0
h) x² + 6x + 9 = 0
⇔ (x + 3)² = 0
⇒ x + 3 = 0
⇔ x = -3
Vậy x = -3
i) x² - 2x + 25x - 50 = 0
⇔ x.(x - 2) + 25.(x - 2) = 0
⇔ (x - 2)(x + 25) = 0
⇔ \(\left[ \begin{array}{l}x - 2 = 0\\x + 25 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 2\\x = -25\end{array} \right.\)
Vậy x ∈ {2; -25}
m) x³ + 3x² + 3x + 1 = 0
⇔ (x + 1)³ = 0
⇒ x + 1 = 0
⇔ x = -1
Vậy x = -1
n) x³ + 6x² + 12x + 8 = 0
⇔ (x + 2)³ = 0
⇒ x + 2 = 0
⇔ x = -2
Vậy x = -2
