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:\(101=100+1=x+1\)

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

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

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

Sai rồi bạn ơi, f(x) =x^10-101x^9+101x^8-101x^7+...-101x+''101'' chứ không phải 100 đâu bạn ơi!

Ta có:

\(x^{10}-\left(100+1\right)x^9+\left(100+1\right)x^8-\left(100+1\right)x^7+.....-\left(100+1\right)x+100+1\)

\(=x^{10}-100x^9-x^9+100x^8+x^8-100x^7-x^7+......-100x-x+100+1\)

\(f\left(x\right)=x^{10}-\left(100+1\right)x^9+\left(100+1\right)x^8-\left(100+1\right)x^7+...-\left(100+1\right)x+100+1\)

\(=x^{10}-100x^9-x^9+100x^8+x^8-100x^7-x^7+...-100x-x+100+1\)

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

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

Ta có: \(f\left(100\right)=\left(100-100\right)\left(100^9-100^8+100^7-...+100-1\right)+1\)

\(=0+1=1\)

Vậy f(100) = 1.

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

-x+25=25?

Ta hiểu tính f(100) thì tính f(x) tại x=100

Ta có:x+1=100+1=101

Thay vào biểu thức thì ta có:

\(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...-101x+30\)

\(f\left(x\right)=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-\left(x+1\right)x^7+...-\left(x+1\right)x+30\)

\(f\left(x\right)=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...-x^2-x+30\)

\(f\left(x\right)=-x+30\)

\(f\left(100\right)=-100+30=-70\)

Vậy f(100)=-70

ai ket bn ko

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