Đặt A = x5 - 2019x4 + 2019x3 - 2019x2 + 2019x - 1000
Ta có: x = 2018 => 2019 = x + 1
=> A = x5 - (x + 1)x4 + (x + 1)x3 - (x + 1)x2 + (x + 1)x - 100
= x5 - x5 -x4 + x4 + x3 - x3 - x2 + x2 + x -1000
= x - 1000 = 2018 - 1000 = 1018
Hướng dẫn:
\(x=2018\Rightarrow2019=x+1\)
Bây giờ cứ chỗ nào có \(2019\) bạn thay nó bằng \(x+1\) là xong thôi
\(=x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-1000\)
\(=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-1000\)
\(=x-1000=1018\)
