Trang chủ » Hỏi đáp » Môn Toán cho f(x)=x^8 – 2016x^7 + 2016x^6 – ….+2016x^2-2016x +1. Tính f(2015) Giúp tớ 29/06/2023 cho f(x)=x^8 – 2016x^7 + 2016x^6 – ….+2016x^2-2016x +1. Tính f(2015) Giúp tớ
Giải đáp: $f\left( {2015} \right) = – 2014$ Lời giải và giải thích chi tiết: $\begin{array}{l}f\left( x \right) = {x^8} – 2016{x^7} + 2016{x^6} – … + \\2016{x^2} – 2016x + 1\\ = {x^8} – 2015{x^7} – {x^7} + 2015{x^6} + …\\ – {x^3} + 2015{x^2} + {x^2} – 2015x – x + 2015 – 2014\\ = {x^7}\left( {x – 2015} \right) – {x^6}\left( {x – 2015} \right) + … – \\{x^2}\left( {x – 2015} \right) + x\left( {x – 2015} \right) – \left( {x – 2015} \right) – 2014\\ = \left( {x – 2015} \right)\left( {{x^7} – {x^6} + … – {x^2} + x – 1} \right) – 2014\\Do:x = 2015\\ \Leftrightarrow x – 2015 = 0\\ \Leftrightarrow f\left( {2015} \right) = 0 – 2014 = – 2014\end{array}$ Trả lời
f\left( x \right) = {x^8} – 2016{x^7} + 2016{x^6} – … + \\
2016{x^2} – 2016x + 1\\
= {x^8} – 2015{x^7} – {x^7} + 2015{x^6} + …\\
– {x^3} + 2015{x^2} + {x^2} – 2015x – x + 2015 – 2014\\
= {x^7}\left( {x – 2015} \right) – {x^6}\left( {x – 2015} \right) + … – \\
{x^2}\left( {x – 2015} \right) + x\left( {x – 2015} \right) – \left( {x – 2015} \right) – 2014\\
= \left( {x – 2015} \right)\left( {{x^7} – {x^6} + … – {x^2} + x – 1} \right) – 2014\\
Do:x = 2015\\
\Leftrightarrow x – 2015 = 0\\
\Leftrightarrow f\left( {2015} \right) = 0 – 2014 = – 2014
\end{array}$