Question

Cho biểu thức M=x²⁰²³-2023(x²⁰²²-x²⁰²¹+x²⁰²⁰-x²⁰¹⁹+...+x²-x)

Tính giá trị của biểu thức M với x=2022

Answer 1

`M=x^2023 - 2023(x^2022-x^2021+x^2020-x^2019+...+x^2-x)`

`=x^2023-2023x^2022+2023x^2021-2023x^2020+2023x^2019-...-2023x^2+2023x`

`=2022^2023-2023*2022^2022+2023*2022^2021-2023*2022^2020+2023*2020^2019-...-2023*2022^2+2023*2022`

`=2022^2023-(2022+1)*2022^2022+(2022+1)*2022^2021-(2022+1)*2022^2020+(2022+1)*2020^2019-...-(2022+1)*2022^2+(2022+1)*2022`

`=2022^2023-2022^2023-2022^2022+2022^2022+2022^2021-2022^2021-2022^2020+2022^2020+2022^2019-...-2022^3-2022^2+2022^2+2022`

`=2022`