Toán CMR: $(2^9+2^7+1)(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1)=2^{32}+1$ 01/08/2021 By Aubrey CMR: $(2^9+2^7+1)(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1)=2^{32}+1$
Ta có : `(2^9+2^7+1)(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1)` `=2^{32}+2^{23}+2^{18}+512-2^{24}-2^{17}+2^{23}-2^{17}-1024+512+1` `=2^{32}+2.2^{23}+2^{18}+1-2^{24}-2.2^{17}` `=2^{32}+2^{14}+2^{18}+1-2^{24}-2^{18}` `=2^{32}+1` `⇒ ĐPCM` Xin hay nhất ! Trả lời
Ta có :
`(2^9+2^7+1)(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1)`
`=2^{32}+2^{23}+2^{18}+512-2^{24}-2^{17}+2^{23}-2^{17}-1024+512+1`
`=2^{32}+2.2^{23}+2^{18}+1-2^{24}-2.2^{17}`
`=2^{32}+2^{14}+2^{18}+1-2^{24}-2^{18}`
`=2^{32}+1`
`⇒ ĐPCM`
Xin hay nhất !