Question

Cho hai số A = (2018^2017 + 2017^2017)^2018 ; B = (2018^2018 + 2017^2018)^2017. so sánh A và B

Answer 1

\(A=\left(2018^{2017}+2017^{2017}\right)^{2018}\) ; \(B=\left(2018^{2018}+2017^{2018}\right)^{2017}\)

Ta có:

\(B=\left(2018.2018^{2017}+2017.2017^{2017}\right)^{2017}\)

\(\Rightarrow B< \left(2018.2018^{2017}+2018.2017^{2017}\right)^{2017}\)

\(\Rightarrow B< \left(2018^{2017}+2017^{2017}\right)^{2017}.2018^{2017}\)

\(\Rightarrow B< \left(2018^{2017}+2017^{2017}\right)^{2017}.\left(2018^{2017}+2017^{2017}\right)\)

\(\Rightarrow B< \left(2018^{2017}+2017^{2017}\right)^{2018}=A\)

\(\Rightarrow B< A\)