Question

Chi P(x)= x¹⁰ - 2010.x^9​ + 2010x⁸ -2010x^7+...+2010x^2-2010x-1

Tính giá trị P(x) tại x=2009

Answer 1

Thay 2010 = x + 1 vào P ( x ),ta có :

\(^{x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-\left(x+1\right)x^7+...+\left(x+1\right)x^2-\left(x+1\right)x-1}\)

= x¹⁰ - x¹⁰ - x⁹ + x⁹ + x⁸ - x⁸ - x⁷ + ... + x³ + x² - x² + x - 1

= x + 1

= 2009 + 1

= 2010
 

Answer 2

Thay 2010 = x+ 1 vào P( x) ,có :

\(x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-\left(x+1\right)x^7+...+\left(x+1\right)x^2-\left(x+1\right)x-1\)

= \(x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^3+x^2-x^2+x-1\) 

= x+1 

= 2009 + 1

= 2010