Câu hỏi của Nguyễn Thu Ngà

Question

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

Nguyễn Việt Lâm · Accepted Answer

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

Ta có:

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

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

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

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

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

$\Rightarrow B< A$Câu trả lời: $A=\left(2018^{2017}+2017^{2017}\right)^{2018}$ ; $B=\left(2018^{2018}+2017^{2018}\right)^{2017}$

Ta có:

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

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

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

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

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

$\Rightarrow B< A$