Question

So sánh : \(\left(26^{2018}+3^{2018}\right)^{2019}\) và \(\left(26^{2019}+3^{2019}\right)^{2018}\)

Answer 1

\(A=\left(26^{2018}+3^{2018}\right)^{2019}\)

\(B=\left(26^{2019}+3^{2019}\right)^{2018}\)

\(B=\left(26^{2018}.26+3.3^{2018}\right)^{2018}< \left(26^{2018}.26+3^{2018}.26\right)^{2018}\)

\(B< \left(26^{2018}+3^{2018}\right)^{2018}.26^{2018}< \left(26^{2018}+3^{2018}\right)^{2018}.\left(26^{2018}+3^{2018}\right)\)

\(\Rightarrow B< \left(26^{2018}+3^{2018}\right)^{2019}\Rightarrow B< A\)