Question

[DQN EDM]

Cho P(x) = x^2019- 1000x^2018 + 1000x^2017- 1000x^2016 +...+ 1000 x - 1.Tính P(999).

Answer 1

[l҉o҉n҉g҉ d҉z҉]

P(x) = x²⁰¹⁹ - 1000x²⁰¹⁸ + 1000x²⁰¹⁷ - 1000x²⁰¹⁶ + ... + 1000x - 1

Với x = 999 => 1000 = x + 1

=> P(999) = x²⁰¹⁹ - ( x + 1 )x²⁰¹⁸ + ( x + 1 )x²⁰¹⁷ - ( x + 1 )x²⁰¹⁶ + ... + ( x + 1 )x - 1

= x²⁰¹⁹ - x²⁰¹⁹ - x²⁰¹⁸ + x²⁰¹⁸ + x²⁰¹⁷ - x²⁰¹⁷ - x²⁰¹⁶ + ... + x² + x - 1

= x - 1 = 999 - 1 = 998

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