(2x - 1)³ - 8x + 4 = 0
(2x - 1)³ - 4x(2x - 1) = 0
(2x - 1)[(2x - 1)² - 4x] = 0
(2x - 1)[(2x - 1)(2x - 1) - 4x] = 0
(2x - 1)[2x(2x - 1) - 1.(2x - 1) - 4x] = 0
(2x - 1)(4x² - 2x - 2x + 1 - 4x) = 0
(2x - 1)(4x² + 1) = 0
⇒ 2x - 1 = 0 hoặc 4x² + 1 = 0
*) 2x - 1 = 0
2x = 1
x = 1/2
*) 4x² + 1 = 0
4x² = -1 (vô lý vì 4x² ≥ 0 với mọi x)
Vậy x = 1/2
`(2x-1)^3-8x+4=0`
`-> (2x-1)^3 - 4(2x-1)=0`
`-> (2x-1)^2*(2x-1)-4(2x-1)=0`
`-> (2x-1)* [(2x-1)^2-4]=0`
`->` TH1: `2x-1=0`
`-> 2x=1`
`-> x=1/2`
TH2: `(2x-1)^2-4=0`
`-> (2x-1)^2=4`
`-> (2x-1)^2=(+-2)^2`
`->`\(\left[{}\begin{matrix}2x-1=2\\2x-1=-2\end{matrix}\right.\)
`->`\(\left[{}\begin{matrix}2x=3\\2x=-1\end{matrix}\right.\)
`->`\(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy, `x={1/2; 3/2; -1/2}`.
