Question

Cho \(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25.\). Tính f(100)

Answer 1

\(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25\)

\(f\left(x\right)=x^8-100x^7-x^7+100x^6+x^6-100x^5-x^5+...+100x^2+x-100x-x+25\)

\(f\left(x\right)=x^7\left(x-100\right)-x^6\left(x-100\right)+x^5\left(x-100\right)-...+x\left(x-100\right)-x+25\)

\(f\left(100\right)=x^7.0-x^6.0+x^5.0-...+x.0-100+25\)

\(f\left(100\right)=25-100=-75\)

Answer 2

\(f\left(100\right)=100^8-101.\left(100^7-100^6+100^5-100^4+100^3-100^2+100\right)+25\)

ta có: \(100.\left(100^7-100^6+...-100^2+100\right)+\left(100^7-100^6+...-100^2+100\right)=100^8+100\)

\(\Rightarrow f\left(x\right)=100^8-100^8-100+25=-75\)

p/s: cách này ngắn nên tớ làm, ko phải câu (có 1 bạn tl rồi)