Tham khảo
Do đó `(2020^{100}+2020^{96}+...+2020^4+1).(2020^4-1)=|x-2020|.(2020^{104}-1)`
Đặt `A= 2020^{100}+2020^{96}+...+2020^4+1`
`⇒2020^{4}A=2020^{104}+2020^{100}+...+2020^{8}+2020^4`
`⇒2020^{4}A-A=2020^{104}+2020^{100}+...+2020^{8}+2020^4-(2020^{100}+2020^{96}+...+2020^4+1)`
`⇒(2020^{4}-1)A=2020^{104}-1`
`⇒A=\frac{2020^{104}-1}{2020^{4}-1}`
Nên `\frac{2020^{104}-1}{2020^{4}-1}×(2020^{4}-1)=|x-2020|.(2020^{104}-1)`
`⇒2020^{104}-1=|x-2020|.(2020^{104}-1)`
`⇒|x-2020|=1`
`⇒`\(\left[ \begin{array}{l}x-2020=1\\x-2020=-1\end{array} \right.\)
`⇒`\(\left[ \begin{array}{l}x=2020+1\\x=-1+2020\end{array} \right.\)
`⇒`\(\left[ \begin{array}{l}x=2021\\x=2019\end{array} \right.\)
Vậy `x=2021` hoặc `x=2019`
`\text{©CBT}`
