Tìm x ∈ N, biết : (2x – 1 )^(2020) = ( 2x – 1 )^(2021)

Đáp án:

`x=1`

Giải thích các bước giải:

`(2x – 1 )^(2020) = ( 2x – 1 )^(2021)`
`=>(2x-1)^2020-(2x-1)^2021=0`
`=>(2x-1)^2020 – (2x-1)^2020 . (2x-1)=0`
`=>(2x-1)^2020 . 1-(2x-1)^2020 .(2x-1)=0`
`=>(2x-1)^2020.[1-(2x-1)]=0`
`=>`\(\left[ \begin{array}{l}(2x-1)^{2020}=0\\1-(2x-1)=0\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}2x-1=0\\2x-1=0+1\end{array} \right.\) 
`=>`\(\left[ \begin{array}{l}2x=0+1\\2x-1=1\end{array} \right.\) 
`=>`\(\left[ \begin{array}{l}2x=1\\2x=1+1\end{array} \right.\) 
`=>`\(\left[ \begin{array}{l}x=1:2\\2x=2\end{array} \right.\) 
`=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=2:2\end{array} \right.\) 
`=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=1\end{array} \right.\) 

Vì `x\inNN` `=>x=1`