Đáp án+Giải thích các bước giải:
`(2x-1)^2018=(2x-1)^2021`
`⇔(2x-1)^2021-(2x-1)^2018=0`
`⇔(2x-1)^{2018}.[(2x-1)^3-1]=0`
`⇔(2x-1)^2018[(2x-1)^3-1^3]=0`
`⇔(2x-1)^{2018}(2x-1-1).[(2x-1)^2+(2x-1).1+1]=0`
`⇔(2x-1)^2018(2x-2)(4x^2-4x+1+2x-1+1)=0`
`⇔(2x-1)^2018(2x-2)(4x^2-2x+1)=0`
TH 1:
`(2x-1)^2018=0`
`⇔2x-1=0`
`⇔2x=1`
`⇔x=1/2`
TH 2:
`2x-2=0`
`⇔2x=2`
`⇔x=1`
TH 3:
`4x^2-2x+1=0`
`⇔4(x^2-1/2x+1/4)=0`
`⇔x^2-1/2x+1/4=0`
`⇔x^2-2.x.(1/4)+1/16+3/16=0`
`⇔(x-1/4)^2+3/16=0`
`⇔(x-1/4)^2=-3/16` (Vô lí)
Vậy `x∈\{1/2;1\}`
`⇒` Chọn `A`
