Đáp án:
`a, x : 12/13 = -26/27`
`⇔ x = -26/27 . 12/13`
`⇔ x = (-26 . 12)/(27 . 13)`
`⇔ x = -24/27`
`⇔ x = -8/9`
Vậy `x = -8/9`
`b, (1/3)^(2x - 1) - (1/3)^2 = -2/27`
`⇔ (1/3)^(2x - 1) - 1/9 = -2/27`
`⇔ (1/3)^(2x - 1) = -2/27 + 1/9 = -2/17 + 3/27`
`⇔ (1/3)^(2x - 1) = 1/27`
`⇔ (1/3)^(2x - 1) = (1/3)^3`
`⇔ 2x - 1 = 3`
`⇔ 2x = 3 + 1 = 4`
`⇔ x = 4 : 2`
`⇒ x = 2`
Vậy `x = 2`
`c, (3 - 1/2 x)(|x + 3/4| - 5/6) = 0`
Suy ra: `3 - 1/2 x = 0` hoặc `|x + 3/4| - 5/6 = 0`
`+` `3 - 1/2 x = 0`
`⇔ 1/2 x = 3 - 0 = 3`
`⇔ x = 3 : 1/2`
`⇔ x = 3 . 2`
`⇔ x = 6`
`+` `|x + 3/4| - 5/6 = 0`
`⇔ |x + 3/4| = 0 + 5/6 = 5/6`
`⇒` $\left[\begin{matrix} x + \dfrac{3}{4} =\dfrac{5}{6} \\ x + \dfrac{3}{4} =\dfrac{-5}{6}\end{matrix}\right.$
`⇒` $\left[\begin{matrix} x =\dfrac{5}{6} - \dfrac{3}{4}\\ x =\dfrac{-5}{6} - \dfrac{3}{4}\end{matrix}\right.$
`⇒` $\left[\begin{matrix} x =\dfrac{1}{12}\\ x =\dfrac{-19}{12}\end{matrix}\right.$
Vậy `x ∈ {6; 1/12 ; -19/12}`
