A(x)=x^21-2019x^20+2019x^19-2018x^18+…+2019x-1 Tính A(2018) 06/08/2021 Bởi Jasmine A(x)=x^21-2019x^20+2019x^19-2018x^18+…+2019x-1 Tính A(2018)
$A(x) = x^{21} – 2019x^{20} + 2019x^{19} – 2019x^{18}+ … + 2019x – 1 \\$ $= x^{21} – ( 2019x^{20} – 2019x^{19} + 2019x^{18}- … – 2019x + 1) \\$ $ A(2018) = x^{21}- [ (x+1)x^{20}- (x+1)x^{19}+ (x+1)x^{18} – … – (x+1)x +1] \\$ $= x^{21} – (x^{21} + x^{20} – x^{20} – x^{19} + x^{19}+ x^{18} – … – x^2 – x + 1) \\$ $= x^{21}- x^{21} + x – 1\\$ $= 2018 – 1= 2017$ Bình luận
Tính `A(2018) => x = 2018 => x- 2018 =0` Ta có: `A(x)= x^21 – 2019x^20 + 2019x^19 -….-2019x^2 + 2019x -1` `A(x)= x^21 – (2018+1)x^20 + (2018+1)x^19 -…-(2018+1)x^2 + (2018+1)x -1` `A(x)= x^21 – 2018x^20 – x^20 + 2018x^19 + x^19 -…-2018x^2 – x^2 + 2018x + x-1` `A(x)= x^20(x-2018) -x^19(x -2018) +….- x(x -2018) + x-1` `A(x)= x^20 . 0 – x^19 .0 +…- x.0 + x-1` `A(x)= x-1` `=> A(2018) = 2018 -1` `=> A(2018)= 2017` Vậy `A(2018)= 2017` Bình luận
$A(x) = x^{21} – 2019x^{20} + 2019x^{19} – 2019x^{18}+ … + 2019x – 1 \\$
$= x^{21} – ( 2019x^{20} – 2019x^{19} + 2019x^{18}- … – 2019x + 1) \\$
$ A(2018) = x^{21}- [ (x+1)x^{20}- (x+1)x^{19}+ (x+1)x^{18} – … – (x+1)x +1] \\$
$= x^{21} – (x^{21} + x^{20} – x^{20} – x^{19} + x^{19}+ x^{18} – … – x^2 – x + 1) \\$
$= x^{21}- x^{21} + x – 1\\$
$= 2018 – 1= 2017$
Tính `A(2018) => x = 2018 => x- 2018 =0`
Ta có:
`A(x)= x^21 – 2019x^20 + 2019x^19 -….-2019x^2 + 2019x -1`
`A(x)= x^21 – (2018+1)x^20 + (2018+1)x^19 -…-(2018+1)x^2 + (2018+1)x -1`
`A(x)= x^21 – 2018x^20 – x^20 + 2018x^19 + x^19 -…-2018x^2 – x^2 + 2018x + x-1`
`A(x)= x^20(x-2018) -x^19(x -2018) +….- x(x -2018) + x-1`
`A(x)= x^20 . 0 – x^19 .0 +…- x.0 + x-1`
`A(x)= x-1`
`=> A(2018) = 2018 -1`
`=> A(2018)= 2017`
Vậy `A(2018)= 2017`