\(\eqalign{
& 2008{\cos ^{2009}}x + 2009{\sin ^{2008}}x = 4017 \cr
& \left\{ \matrix{
{\cos ^{2009}}x \le 1 \Rightarrow 2008{\cos ^{2009}}x \le 2008 \hfill \cr
{\sin ^{2008}}x \le 1 \Rightarrow 2009{\sin ^{2008}}x \le 2009 \hfill \cr} \right. \cr
& \Rightarrow VT \le 4017 \cr
& Dau\,\,'' = ''\,\,xay\,\,ra \cr
& \Leftrightarrow \left\{ \matrix{
{\cos ^{2019}}x = 1 \hfill \cr
{\sin ^{2018}}x = 1 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
\cos x = 1 \hfill \cr
\left[ \matrix{
\sin x = 1 \hfill \cr
\sin x = - 1 \hfill \cr} \right. \hfill \cr} \right.\,\,\left( {Vo\,\,nghiem} \right) \cr} \)
Vậy phương trình đã cho vô nghiệm.
