Toán C(x)=x^21-2004x^20+2004x^19+…+2004x-1. Tại x=-2003 11/09/2021 By Mary C(x)=x^21-2004x^20+2004x^19+…+2004x-1. Tại x=-2003
Giải thích các bước giải: Ta có: $C(x)=x^{21}-2004x^{20}+2004x^{19}+…+2004x-1$ $\to xC(x)=x^{22}-2004x^{21}+2004x^{20}+…+2004x^2-x$ $\to xC(x)-C(x)=x^{22}-2005x^{21}-4008x^{20}-2005x+1$ $\to (x-1)C(x)=x^{22}-2005x^{21}-4008x^{20}-2005x+1$ $\to C(x)\dfrac{x^{22}-2005x^{21}-4008x^{20}-2005x+1}{x-1}$ Tại $x=-2003$ ta có: $\to C(x)\dfrac{(-2003)^{22}-2005\cdot (-2003)^{21}-4008\cdot (-2003)^{20}-2005\cdot (-2003)+1}{-2003-1}$ $\to C(x)\dfrac{2003^{22}+2005\cdot 2003^{21}-4008\cdot 2003^{20}+2005\cdot2003+1}{-2004}$ Trả lời
Giải thích các bước giải:
Ta có:
$C(x)=x^{21}-2004x^{20}+2004x^{19}+…+2004x-1$
$\to xC(x)=x^{22}-2004x^{21}+2004x^{20}+…+2004x^2-x$
$\to xC(x)-C(x)=x^{22}-2005x^{21}-4008x^{20}-2005x+1$
$\to (x-1)C(x)=x^{22}-2005x^{21}-4008x^{20}-2005x+1$
$\to C(x)\dfrac{x^{22}-2005x^{21}-4008x^{20}-2005x+1}{x-1}$
Tại $x=-2003$ ta có:
$\to C(x)\dfrac{(-2003)^{22}-2005\cdot (-2003)^{21}-4008\cdot (-2003)^{20}-2005\cdot (-2003)+1}{-2003-1}$
$\to C(x)\dfrac{2003^{22}+2005\cdot 2003^{21}-4008\cdot 2003^{20}+2005\cdot2003+1}{-2004}$