\(x_1+x_2+x_3+........+x_{49}+x_{50}+x_{51}=0\)
\(\Rightarrow\left(x_1+x_2\right)+\left(x_3+x_4\right)+...........+\left(x_{49}+x_{50}\right)+x_{51}=0\)
Theo bài ra ta có: \(1+1+1+.......+1+x_{51}=0\) \(\Rightarrow1\times25+x_{51}=0\) \(\Rightarrow x_{51}=-25\)
mà \(x_{50}+x_{51}=0\Rightarrow x_{50}+\left(-25\right)=1\Rightarrow x_{50}=26\)