Question

Tính giá trị của đa thức f(x) tại x=11, biết f(x) = \(x^{17}-12x^{16}+12x^{15}-12x^{14}+...+12x-1\)

Answer 1

Tại x=11

\(\Rightarrow f\left(x\right)=x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-...+\left(x+1\right)x-1\)

\(f\left(x\right)=x^{17}-x^{17}-x^{16}+x^{16}+x^{15}-...+x^2+x-1\)

\(f\left(x\right)=x-1\)

\(f\left(x\right)=10\)

Answer 2

\(x=11\Leftrightarrow12=x+1\)

Mà \(f\left(x\right)=x^{17}-12x^{16}+12x^{15}-12x^{14}+........+12x-1\)

\(\Leftrightarrow f\left(x\right)=x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-.......+\left(x+1\right)x-1\)

\(\Leftrightarrow f\left(x\right)=x^{17}-x^{17}-x^{16}+x^{16}+x^{15}-.....+x^2+x-1\)

\(\Leftrightarrow f\left(x\right)=x-1\)

Mà \(x=11\)

\(\Leftrightarrow f\left(11\right)=11-1=10\)

Vậy \(f\left(11\right)=10\)