Question

So sánh a và b biết a=2015^2016-2015^2015 ; b=2015^2017-2015^2016

 

Answer 1

\(A=2015^{2016}-2015^{2015}\)

\(=2015^{2015}\left(2015-1\right)\)

\(=2015^{2015}.2014\)

\(B=2015^{2017}-2015^{2016}\)

\(=2015^{2016}\left(2015-1\right)\)

\(=2015^{2016}.2014\)

Vì    \(2015^{2015}< 2015^{2016}\)

nên   \(A< B\)

Answer 2

Ta có : 

\(2015^{2016}< 2015^{2017}\)

\(2015^{2015}< 2015^{2016}\)

\(\Rightarrow\)\(A=2015^{2016}-2015^{2015}< B=2015^{2017}-2015^{2016}\)

Vậy \(A< B\)