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![](https://rs.olm.vn/images/avt/0.png?1311)
\(7^{20}+49^{11}+343^7\)
\(=7^{20}+\left(7^2\right)^{11}+\left(7^3\right)^7\)
\(=7^{20}+7^{22}+7^{21}\)
\(=7^{20}\left(1+7^2+7\right)\)
\(=7^{20}.57⋮57\)
\(\Leftrightarrowđpcm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
720 + 4911 + 3437 = ( 71 )20 + ( 72 )11 + ( 73 )7 =720 + 721 + 722 = 720 ( 1 + 7 + 72 ) = 720.57
Vì 57 chia hết cho 57 nên 720 .57 chia hết cho 57
=> 720 + 4911 + 3437 chia hết cho 57 ( đpcm )
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\left(\dfrac{2}{7}\right)^2-\dfrac{4}{343}}=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{\dfrac{8}{2}-\dfrac{4}{7}+\dfrac{4}{49}-\dfrac{4}{343}}=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4-\dfrac{4}{7}+\dfrac{4}{49}-\dfrac{4}{343}}=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4\left(1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}\right)}=\dfrac{1}{4}\)
720 + 4911 + 3437
= 720 + (72)11 + (73)7
= 720 + 722 + 721
= 720 + 720 + 2 + 720 + 1
= 720 + 720.72 + 720.7
= 720(1 + 72 + 7)
= 720.57
Vì 57 ⋮ 57 nên 720.57 ⋮ 57
Hay 720 + 4911 + 3437 ⋮ 57
mình biết làm rồi