Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left( {{x^{2018}} + {y^{2018}}} \right) - \left( {{x^{2017}}y + x{y^{2017}}} \right)\\
= {x^{2018}} + {y^{2018}} - {x^{2017}}y - x{y^{2017}}\\
= {x^{2017}}\left( {x - y} \right) + {y^{2017}}\left( {y - x} \right)\\
= \left( {x - y} \right)\left( {{x^{2017}} - {y^{2017}}} \right)\\
= {\left( {x - y} \right)^2}\left( {{x^{2016}} + {x^{2015}}y + {x^{2014}}{y^2} + .... + x{y^{2015}} + {y^{2016}}} \right) \ge 0,\,\,\,\,\,\forall x,y\\
\Rightarrow {x^{2018}} + {y^{2018}} \ge {x^{2017}}y + x{y^{2017}}\\
2\left( {{x^{2017}} + {y^{2017}}} \right) = \left( {x + y} \right)\left( {{x^{2017}} + {y^{2017}}} \right)\\
= \left( {{x^{2018}} + {y^{2018}}} \right) + \left( {{x^{2017}}y + x{y^{2017}}} \right) \le 2\left( {{x^{2018}} + {y^{2018}}} \right)\\
\Rightarrow {x^{2017}} + {y^{2017}} \le {x^{2018}} + {y^{2018}}
\end{array}\)
