Tính `A = x^100 – 2019x^99 – 2019x^98 – … – 2019x^2 – 2019x – 1` tại `x = 2020` 06/09/2021 Bởi Camila Tính `A = x^100 – 2019x^99 – 2019x^98 – … – 2019x^2 – 2019x – 1` tại `x = 2020`
Đáp án + Giải thích các bước giải: Vì `x= 2020 \ to \ x-2020 =0` Ta có : `A= x^100 – 2019x^99 – 2019x^98 – … – 2019x^2 – 2019x -1` `= x^100 – (2020 -1)x^99 – (2020-1)x^98-….-(2020-1)x^2-(2020-1)x -1` `= x^100 – 2020x^99 + x^99 – 2020x^98 + x^98 -…-2020x^2 + x^2 -2020x+ x -1` `= x^99 . (x -2020) + x^98 . (x-2020) +…+ x . (x-2020) + x – 1` `= x^99 . 0 + x^98 . 0 + … + x . 0 + x – 1` `= x – 1` Thay `x= 2020` vào `A` ta được : `A= 2020-1= 2019` Vậy `A= 2019` Bình luận
Từ `x= 2020` `=> x-2020 =0` Ta có: `A= x^100 – 2019x^99 – 2019x^98-…-2019x^2 -2019x -1` `A= x^100 – (2020 -1)x^99 – (2020-1)x^98-….-(2020-1)x^2-(2020-1)x -1` `A= x^100 – 2020x^99 + x^99 – 2020x^98 + x^98 -…-2020x^2 + x^2 -2020x+ x -1` `A= x^99(x -2020) + x^98(x-2020) +…+x(x-2020) + x-1` `A= x^99 . 0 + x^98.0 +…+x.0 + x-1` `A= x-1` Thay `x= 2020` vào `A` ta được: `A= 2020-1` `A= 2019` Vậy `A= 2019` Bình luận
Đáp án + Giải thích các bước giải:
Vì `x= 2020 \ to \ x-2020 =0`
Ta có : `A= x^100 – 2019x^99 – 2019x^98 – … – 2019x^2 – 2019x -1`
`= x^100 – (2020 -1)x^99 – (2020-1)x^98-….-(2020-1)x^2-(2020-1)x -1`
`= x^100 – 2020x^99 + x^99 – 2020x^98 + x^98 -…-2020x^2 + x^2 -2020x+ x -1`
`= x^99 . (x -2020) + x^98 . (x-2020) +…+ x . (x-2020) + x – 1`
`= x^99 . 0 + x^98 . 0 + … + x . 0 + x – 1`
`= x – 1`
Thay `x= 2020` vào `A` ta được :
`A= 2020-1= 2019`
Vậy `A= 2019`
Từ `x= 2020` `=> x-2020 =0`
Ta có:
`A= x^100 – 2019x^99 – 2019x^98-…-2019x^2 -2019x -1`
`A= x^100 – (2020 -1)x^99 – (2020-1)x^98-….-(2020-1)x^2-(2020-1)x -1`
`A= x^100 – 2020x^99 + x^99 – 2020x^98 + x^98 -…-2020x^2 + x^2 -2020x+ x -1`
`A= x^99(x -2020) + x^98(x-2020) +…+x(x-2020) + x-1`
`A= x^99 . 0 + x^98.0 +…+x.0 + x-1`
`A= x-1`
Thay `x= 2020` vào `A` ta được:
`A= 2020-1`
`A= 2019`
Vậy `A= 2019`