Question

cho f(x) = \(x^8\) - 101\(x^7\) + 101\(x^6\) - 101\(x^5\) + ... + 101\(x^2\) - 101 + 25 
tính f(100)

Answer 1

Ta có:\(f\left(x\right)=x^8-100x^7-x^7+100x^6-....+x^2-100x-x+100-75\)

\(=x^7\left(x-100\right)-x^6\left(x-100\right)-....+x\left(x-100\right)-\left(x-100\right)-75\)

Nên \(f\left(100\right)=x^7.\left(100-100\right)-x^6\left(100-100\right)-....+x\left(100-100\right)-\left(100-100\right)-75\)

\(=-75\)

Answer 2

Với x= 100 thì 101=x+1 nên ta có f(100)=x\(^8\)-(x+1)x\(^7\)=(x+1)x\(^6\)-(x+1)x\(^5\)+....-(x+1)+25=x\(^8\)-x\(^8\)+x\(^7\)-......-x-1+25=24