Question

cho A(x)=x^99-109x^98+x^98-109x^97+x^97-109x^96+...+x-109

Tính A(109)

cho B(x)=x^49-10x^48+10x^47-10x^46+...+10x-1

Tính B(9)

cho C(x)=x^999-1000x^998+1000x^997-1000x^996+...+1000x-1

Tính C(999)

Giúp mình với!mai thi rồi

Answer 1

a: \(A\left(109\right)=x^{99}-x^{98}\cdot x+x^{98}-x^{97}\cdot x+...+x-x\)

\(=x^{99}-x^{99}+x^{98}-x^{98}+...+0\)

=0

b: x=9 nên x+1=10

\(B\left(x\right)=x^{49}-x^{48}\left(x+1\right)+x^{47}\left(x+1\right)-...+x\left(x+1\right)-1\)

\(=x^{49}-x^{49}-x^{48}+x^{48}+...+x^2+x-1\)

=x-1=8

c: x=999 nên x+1=1000

\(C\left(x\right)=x^{999}-x^{998}\left(x+1\right)+x^{997}\left(x+1\right)-...+x\left(x+1\right)-1\)

\(=x^{999}-x^{999}-x^{998}+x^{998}+...+x^2+x-1\)

=x-1=998