Question

Tìm f(10) biết f(x) = x¹⁰ - 11x⁹ + 11x⁸ - 11x⁷ + ... + 11x² - 11x + 100 

Answer 1

 

thay 11=x+1 ta có:

f(x)= \(x^{10}\)-11\(x^9\)+11\(x^8\)-11\(x^7\)+....+11\(x^2\)-11x+100

     =\(x^{10}\)-(x+1)\(x^9\)+(x+1)\(x^8\)-(x+1)\(x^7\)+...+(x+1)\(x^2\)-(x+1)x+100

     =\(x^{10}\)-\(x^{10}\)-\(x^9\)+\(x^9\)+\(x^8\)-\(x^8\)-\(x^7\)+......+\(x^3\)+\(x^2\)-\(x^2\)-x+100

     =-x+100

=> f(10)=-10+100=90      

Answer 2

Thay 11 = x + 1 ta có:

f(x) = \(x^{10}-11x^9+11x^8-11x^7+...+11x^2-11x+100\)

      \(=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-\left(x+1\right)x^7+...+\left(x+1\right)x^2-\left(x+1\right)x^2-\left(x+1\right)x+100\)

      = \(x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^3+x^2-x^2-x+100\)

      = -x+100

=>f(10)= - 10 + 100 = 90