Question

Cho đa thức f(x)=x⁸-101x⁷+101x⁶-101x⁵+....101x²-101x+25

Tính f(100)

Giải nhanh mk tik cho

Answer 1

\(f\left(100\right)\Rightarrow x=100\)

\(\Rightarrow x+1=101\)

Thay x + 1 = 101 ta được:

\(f\left(100\right)-x^8-\left(x+1\right)x^7+\left(x+1\right)x^6-\left(x+1\right)x^5+...+\left(x+1\right)x^2-\left(x+1\right)x+25\)

\(=x^8-\left(x^8+x^7\right)+\left(x^7+x^6\right)-\left(x^6+x^5\right)+...+\left(x^3+x^2\right)-\left(x^2+x\right)+25\)

\(=x^8-x^8-x^7+x^7+x^6-x^6-x^5+...+x^3+x^2-x^2-x+25\)

\(=-x+25\)

\(=-100+25\)

\(=-75\)

Answer 2

Thank you very much