Toán Lớp 7: f(=(x))=x^10-2017x^9-2017x^8=2017x-1 biết x=2018

Question

Toán Lớp 7:  f(=(x))=x^10-2017x^9-2017x^8-....-2017x-1 biết x=2018

tuenhioanh · Answer

Giải đáp:   $  $   Biết x=2018   -> x - 1 = 2017 (1)   C&oacute; : f (x) = x^{10} - 2017 x^9 - 2017 x^8 - ... - 2017x - 1   Thay (1) v&agrave;o ta được :   -> f (x) = x^{10} - (x-1)x^9 - (x-1)x^8 - ... - (x-1)x-1   ->f (x) =x^{10} - x^{10} + x^9 - x^9 + x^8 - ... - x^2 + x - 1   -> f (x) = (x^{10}-x^{10}) + (x^9 - x^9) + ... + (x^2-x^2) + (x-1)   -> f (x)=x-1   -> f (2018) = 2018-1   -> f (2018) = 2017   vậy f (2018) = 2017

hoaiphuong85 · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    Thay x=2018 v&agrave;o f(x) ta c&oacute; :    f(2018) = $2018^{10}$ - $2017$ . $2018^{9}$ - $2017$ . $2018^{8}$ -...- $2017$ . $2018$ - $1$    = $2018^{10}$ - ($2018$ - $1$) . $2018^{9}$ - ($2018$ - $1$) . $2018^{8}$ -....- ($2018$ - $1$) . $2018$ - $1$    = $2018^{10}$ - $2018^{10}$ + $2018^{9}$ - $2018^{9}$ + $2018^{8}$ - $2018^{8}$ +....+ $2018^{2}$ - $2018^{2}$ + $2018$ - $1$    = $2018$ - $1$    = $2017$    Vậy f(2018)=2017    $ text{Nocopy}$    $ textit{@gladbach}$