Question

[Trần Khánh Linh]

 tìm x biết (x-1)²⁰²⁰=(x-1)²⁰²²

Answer 1

[Dora]

`(x-1)^{2020}=(x-1)^{2022}`

`<=>(x-1)^{2022}-(x-1)^{2020}=0`

`<=>(x-1)^{2020}[(x-1)^{2}-1]=0`

`@TH1: (x-1)^{2020}=0<=>x-1=0<=>x=1`

`@TH2: (x-1)^{2}-1=0<=>(x-1)^{2}=1`

                        `<=>x-1=1` hoặc `x-1=-1`

                        `<=>x=2`     hoặc `x=0`

Answer 2

[Trần Phương Thảo]

\(\left(x-1\right)^{2020}=\left(x-1\right)^{2022}\)

⇒\(\left(x-1\right)^{2020}-\left(x-1\right)^{2022}=0\)

⇒\(\left(x-1\right)^{2020}\cdot\left[1-\left(x-1\right)^2\right]=0\)

+) \(\left(x-1\right)^{2020}=0\)

     \(\Leftrightarrow x=1\)

+) \(1-\left(x-1\right)^2=0\)

     \(\Leftrightarrow\left(x-1\right)^2=1\)

      \(\Leftrightarrow x-1=1hoặcx-1=-1\)

      \(\Leftrightarrow x=2hoặcx=0\)