Cho
f(x)=x8 -101x7+101x6-101x5+...+101x2 -101x +25 . Tính f(100)
cho f(x)=x8-1017+101x6-101x5+......+101x2-101x+25
tính f(100)
Ta có: x=100
nên x+1=101
Ta có: \(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25\)
\(=x^8-x^7\left(x+1\right)+x^6\left(x+1\right)-x^5\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+25\)
\(=x^8-x^7-x^7+x^7+x^6-x^6-x^5+x^5-x^4+...+x^3+x^2-x^2-x+25\)
\(=-x+25\)
\(=-100+25=-75\)
Cho đa thức f(x)=x10-101x9+101x8-101x7+...+101x+2021. Tính f(100)
Ta có: x=100
\(\Leftrightarrow x+1=101\)
Ta có: \(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...+101x+2021\)
\(=x^{10}-x^9\cdot\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x\left(x+1\right)+2021\)
\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^2+x+2021\)
\(=x+2021\)
\(=100+2021=2121\)
cho f(x)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25.Tính f(100)
Cho đa thức f(x)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25. Tính f(100)
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
Cho F(x) = x^8 -101x^7+101x^6-101x^5+...+101x^2-101x+25
Tính F(100)
Cho đa thức f(x) + x^8 - 101x^7+101x^6-101x^5+...+101x^2-101x+25 . Tính f(100)
cho đa thức f(x)=x^8-101x^7+101x^6-101x^5+...+101x+25
Tính f(100)
Cho f(x)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25
Tính f(100)
f(100)=> x=100
=>x+1=101
thay x+1=101 ta được:
f(100)=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
=x8-x8-x7+x7+x6-x6-x5+...+x3+x2-x2-x+25
=-x+25
=-100+25
=-75
Cho f(x)=x^8-101x^7+101x^6-101x^5+....+101x^2+101x+25
Tính f(100)
\(x=100\Rightarrow x+1=101\)
\(f\left(x\right)=x^8-\left(x+1\right).x^7+\left(x+1\right).x^6-\left(x+1\right).x^5+....+\left(x+1\right).x^2+\left(x+1\right).x+25\)
\(f\left(x\right)=x^8-x^8-x^7+x^7+x^6-x^6-x^5+.....+x^3+x^2-x^2+x+25\)
\(f\left(100\right)=100+25=125\)
f(x)=101x^8-101x^7+101x^6-...+101x^2-101x+25 Tính f(100)