Đáp án+Giải thích các bước giải:
`a) (4x - 1)^2 - (3x + 2)^2 = 0`
`⇒ (4x - 1 - 3x - 2) . (4x - 1 + 3x + 2) = 0`
`⇒ [(4x - 3x) - 1 - 2] . [(4x + 3x) - 1 + 2] = 0`
`⇒ (x - 3) . (7x + 1) = 0`
`⇒` $\left[\begin{matrix} x - 3 = 0\\ 7x + 1 = 0\end{matrix}\right.$
`⇒` $\left[\begin{matrix} x = 3\\ 7x = -1\end{matrix}\right.$
`⇒` $\left[ \begin{array} xx = 3\\x=\frac{-1}{7}\end{array}\right.$
Vậy: `x = {3 ; -1/7}`
`b) 27x^3 - 54x^2 + 36x - 8 = 0`
`⇒ (3x - 2)^3 = 0`
`⇔ 3x - 2 = 0`
`⇒ 3x = 2`
`⇒ x = 2/3`
Vậy: `x = 2/3`
`c) 1 - 9x^2 = (3x + 1)^2`
`⇒ (1 + 3x) . (1 - 3x) - (3x + 1)^2 = 0`
`⇒ (3x + 1) . (1 - 3x - 3x - 1) = 0`
`⇒ (3x + 1) - 6x = 0`
`⇒` $\left[\begin{matrix} 3x + 1 = 0\\ -6x = 0\end{matrix}\right.$
`⇒` $\left[\begin{matrix} 3x = -1\\ x = 0\end{matrix}\right.$
`⇒` $\left[ \begin{array}xx = \frac{-1}{3}\\x=0\end{array}\right.$
Vậy: `x = {-1/3 ; 0}`
`d) x^3 + 3/2x^2 + 3/4x + 1/8 = 1/69`
`⇒ (x + 1/2)^3 = (1/4)^3`
`⇔ x + 1/2 = 1/4`
`⇒ x = 1/4 - 1/2`
`⇒ x = 1/4 - 2/4`
`⇒ x = -1/4`
Vậy: `x = -1/4`
