Toán rút gọ biểu thức sau : P = 12(5^2 + 1 )(5^4 +1 )(5^8 +1)(5^16+1) 22/09/2021 By Gianna rút gọ biểu thức sau : P = 12(5^2 + 1 )(5^4 +1 )(5^8 +1)(5^16+1)
P= 12($5^{2}$ + 1 )($5^{4}$ +1 )($5^{8}$ +1)($5^{16}$+1) 2P = 24.(5^2 + 1 )(5^4 + 1) … (5^16 + 1) 2P = (5^2 – 1) (5^2 + 1) (5^4 + 1) .. (5^16+1) 2P = (5^4 – 1 )(5^4 + 1 ) (5^8 + 1) 2P = (5^8 – 1 ) (5^8 + 1) (5^16 + 1) 2P = ( 5^ 16 – 1 ) 5^ 16 + 1) 2P = 5^32 – 1 P = (5^32 – 1) : 2 Trả lời
`P=12.(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)` `⇒2P=24.(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)` `⇒2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)` `⇒2P=(5^4-1)(5^4+1)(5^8+1)(5^{16}+1)` `⇒2P=(5^8-1)(5^8+1)(5^{16}+1)` `⇒2P=(5^{16}-1)(5^{16}+1)` `⇒2P=5^{32}-1` `⇒P=\frac{5^{32}-1}{2}` Trả lời
P= 12($5^{2}$ + 1 )($5^{4}$ +1 )($5^{8}$ +1)($5^{16}$+1)
2P = 24.(5^2 + 1 )(5^4 + 1) … (5^16 + 1)
2P = (5^2 – 1) (5^2 + 1) (5^4 + 1) .. (5^16+1)
2P = (5^4 – 1 )(5^4 + 1 ) (5^8 + 1)
2P = (5^8 – 1 ) (5^8 + 1) (5^16 + 1)
2P = ( 5^ 16 – 1 ) 5^ 16 + 1)
2P = 5^32 – 1
P = (5^32 – 1) : 2
`P=12.(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)`
`⇒2P=24.(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)`
`⇒2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)`
`⇒2P=(5^4-1)(5^4+1)(5^8+1)(5^{16}+1)`
`⇒2P=(5^8-1)(5^8+1)(5^{16}+1)`
`⇒2P=(5^{16}-1)(5^{16}+1)`
`⇒2P=5^{32}-1`
`⇒P=\frac{5^{32}-1}{2}`