So sánh 72^45-72^44va72^44-72^43
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\(72^{45}-72^{44}\)và \(72^{44}-72^{43}\)
Ta có : \(72^{45}-72^{44}=72.72^{44}-72^{44}=72^{44}\left(72-1\right)=72^{44}.71.\)
\(\)\(72^{44}-72^{43}=72.72^{43}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71.\)
Vì \(72^{44}.71>72^{43}.71\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}.\)
VẬY .....
72^45-72^44 = 72^44 (72-1)
72^44-72^43 = 72^43 ( 72 -1 )
vì 72^44>72^43 => 72^44(72-1)>72^43(72-1)
Hay 72^45-72^44 > 72^44-72^43
\(72^{45}-72^{44}=72^{1+44}-72^{44}=72.72^{44}-72^{44}=\left(72-1\right).72^{44}=71.72^{44}\)
\(72^{44}-72^{43}=72^{1+43}-72^{43}=72.72^{43}-72^{43}=\left(72-1\right).72^{43}=71.72^{43}\)
Ta thấy \(71.72^{44}>71.72^{43}\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}.\)
72^45 - 72^44 = 72^44 . 71
72^44 - 72^43 = 72^43 . 71
Vì 72^44 > 72^43
nên 72^44 . 71 > 72^43 . 71
==> A>B
7245-7244=7244.(72-1)=7244.71
7244-7243=7243.(72-1)=7243.71
Do 7244.71>7243.71
Nên 7245-7244>7244-7243
đặt A=72^45-72^44=72^44.(72-1) (1)
B=72^44-72^43=72^43.(72-1) (2)
từ 1 và 2 => A>B
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\(72^{45}-72^{44}=72^{44}.7-72^{44}.1=72^{44}\left(7-1\right)=72^{44}.6\)
\(72^{44}-72^{43}=72^{43}.7-72^{43}.1=72^{43}\left(7-1\right)=72^{43}.6\)
\(\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
Ta có :
\(72^{45}-72^{44}=72^{44}\left(72-1\right)=7^{44}.71\)
\(72^{44}-72^{43}=72^{43}\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}.71>7^{43}.71\)
\(\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
72^45 - 72^44 = 72^44 ( 72 - 1 ) = 72^44 . 71
72^44 - 72^43 = 72^43 ( 72 - 1 ) = 72^43 . 71
Vì 44 > 43 nên 72^44 . 71 > 72^43 . 71 hay 72^45 - 72^44 > 72^44 - 72^43