13591 - 13589 = 13589 x ( 1352 - 1 )
135100 - 13599 = 13599 x ( 135 - 1 ) = 13599 x 134 = 13589 x 13510 x 134 = 13589 x ( 13510 x 134 )
Có : 1352 - 1 < 13510 x 134
=> 13589 x ( 1352 - 1 ) < 13589 x ( 13510 x 134 )
=> 13591 - 13589 < 135100 - 13599
Ta có:
\(135^{91}-135^{89}=135^{89}\times\left(135^2-1\right)\)
\(135^{100}-135^{99}=135^{99}\times\left(135-1\right)=135^{99}\times134=135^{89}\times134=135^{89}\times\left(135^{10}\times34\right)\)
Có: \(135^2-1< 135^{10}\times134\)
\(\Rightarrow135^{89}\times\left(135^2-1\right)< 135^{89}\times\left(135^{10}\times134\right)\)
\(\Rightarrow135^{91}-135^{89}< 135^{100}-135^{99}\)
Vậy \(135^{91}-135^{89}< 135^{100}-135^{99}\)
