so sánh hai biểu thức
A= 72^45- 72^44
B=72^44-72^43
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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 \(71.72^{44}>71.72^{43}\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}.\)
\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}>72^{41}\Rightarrow72^{44}.71>72^{43}.71\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
Theo đề bài ta có:
7245 - 7244 = 7244 x ( 72 - 1 ) = 7244 x 71
7244 - 7243 = 7243 x ( 72 - 1 ) = 7243 x 71
Mà 7244 > 7243 ; 71 = 71
=> 7245 - 7244 > 7244 - 7243
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 \(72^{44}.71>7^{43}.71\)
\(\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
Ta có: \(72^{45}-72^{44}=72^{44}\left(72-1\right)\)
\(72^{44}-72^{43}=72^{43}\left(72-1\right)\)
=> \(72^{44}\left(72-1\right)>72^{43}\left(72-1\right)\) hay \(72^{45}-72^{44}>72^{44}-72^{43}\)
T_i_c_k nha
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
A=72^45-72^44=72^44(72-1)=72^44x71
B=72^43x71
=>A>B