Question

Tính giá trị biểu thức :

a, N = \(x^6-2017x^5+2017x^4-2017x^3+2017x^2-2017x+2025\)

tại x = 2016

b, Q = \(2017x^{2016}+2016x^{2015}+2015x^{2014}+...+3x^2+2x+1\)

tại x = ( -1 )

Answer 1

a/ Với \(x=2016\Rightarrow2017=x+1\)

\(A=x^6-\left(x+1\right)x^5+\left(x+1\right)x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+2025\)

\(A=x^6-x^6-x^5+x^5+x^4-x^4-x^3+x^3+x^2-x^2-x+2025\)

\(A=2025-x=9\)

b/ Với \(x=-1\Rightarrow\left\{{}\begin{matrix}x^{2k}=1\\x^{2k+1}=-1\end{matrix}\right.\) ta có:

\(Q=2017-2016+2015-2014+...+3-2+1\)

\(Q=1+1+1+...+1+1\) (có \(\frac{2016}{2}+1=1009\) số 1)

\(Q=1009\)