Question

Cho x₁ + x₂ +x₃+..........+x₂₀₁₆ + x₂₀₁₇ = 0 và x₁ + x₂ = x₃ + x₄ = x₅ + x₆ = .......... = x₂₀₁₅ +x₂₀₁₆ = x₂₀₁₆ + x₂₀₁₇ = 1

Tìm x₂₀₁₆

Answer 1

Ta có: \(\left\{{}\begin{matrix}x_1+x_2+x_3+...+x_{2016}+x_{2017}=0\\x_1+x_2=x_3+x_4=x_5+x_6=...=x_{2015}+x_{2016}=x_{2016}+x_{2017}=1\end{matrix}\right.\)

Từ \(x_1+x_2+x_3+...+x_{2016}+x_{2017}=0\)

\(\Rightarrow\left(x_1+x_2\right)+\left(x_3+x_4\right)+...+\left(x_{2015}+x_{2016}\right)+x_{2017}=0\)

\(\Rightarrow1+1+...+1+x_{2017}=0\)

\(\Rightarrow1008+x_{2017}=0\Leftrightarrow x_{2017}=-1008\)

Mà \(x_{2016}+x_{2017}=1\Leftrightarrow x_{2016}=1-x_{2017}=1009\)