Ta có: x=100

nên x+1=101

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

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

\(=x^8-x^7-x^7+x^7+x^6-x^6-x^5+x^5-x^4+...+x^3+x^2-x^2-x+25\)

\(=-x+25\)

\(=-100+25=-75\)

hơi khó hỉu

Ta có: x=100

\(\Leftrightarrow x+1=101\)

Ta có: \(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...+101x+2021\)

\(=x^{10}-x^9\cdot\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x\left(x+1\right)+2021\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^2+x+2021\)

\(=x+2021\)

\(=100+2021=2121\)

f(100)=x⁸-(100+1)x⁷+(100+1)x⁶-(100+1)x⁵+....+(100+1)x²-(100+1)x+25

=x⁸-(x+1)x⁷+(x+1)x⁶-(x+1)x⁵+....+(x+1)x²-(x+1)x+25

=x⁸-x⁸-x⁷+x⁷+x⁶-x⁶-x⁵+...+x³+x²-x²-x+25

=25

vậy f(100)=25

Mk ko hiểu lắm! Hoàng Phúc

ai ket bn ko

giải hộ

Ta có : x=100=>101=x+1

Thay vào f(x), ta được : x¹⁰ -(x+1)x⁹ +(x+1)x⁸ - (x+1)x⁷ +....-(x+1)x +100

                               <=> x¹⁰ - x¹⁰ -x⁹ +x⁹ + x⁸ -x⁸ -x^{7 +.... -}x² -x +100

                               <=> -x+100 

                                => f(100) = -x+100=-100+100=0

ta có :

\(f\left(x\right)=x^{10}-101x^9+101x^8-...-101x+101\)

\(=x^{10}-x^9-100x^9+x^8+100x^8-...-x-100x+100+1\)

ta có :

\(f\left(100\right)=100^{10}-100^9-100\times100^9+100^8+100\times100^8-...-100-100\times100+100+1\)

\(=100^{10}-100^{10}-100^9+100^9+100^8-...-100^2-100+100+1\)

\(=1\)

vậy f(100)=1

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

\(\Rightarrow x+1=101\)

Thay x + 1 = 101 ta được:

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

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

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

\(=-x+25\)

\(=-100+25\)

\(=-75\)

Thank you very much

Ta có: 

\(F\left(100\right)=100^{10}-101.100^9+101.100^8-101.100^7+...-101.100+101\)

       \(=100-\left(100+1\right).100^9+\left(100+1\right).100^8-\left(100+1\right).100^7+...-\left(100+1\right).100+101\)

 \(=100^{10}-100^{10}-100^9+100^9+100^8-100^8-100^7+...-100^2-100+101\)

\(=1\)

Ta có:\(101=100+1=x+1\)

\(\Rightarrow F\left(100\right)=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-...-\left(x+1\right)x+x+1\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-...-x^2-x+x+1=1\)