Đáp án:
Giải thích các bước giải:
a) `(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)`
`=3(2^2+1)(2^4+1)(2^8+1)(2^16+1)`
`=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)`
`=(2^4-1)(2^4+1)(2^8+1)(2^16+1)`
`=(2^8-1)(2^8+1)(2^16+1)`
`=(2^16-1)(2^16+1)`
`=2^32-1` (đpcm) (đề thiếu -1 nhé)
b) xét hiệu:
`100^2+103^2+105^2+94^2-101^2-98^2-96^2-107^2`
`=(100^2-98^2)+(103^2-101^2)-(107^2-105^2)-(96^2-94^2)`
`=(100-98)(100+98)+(103-101)(103+101)-(107-105)(107+105)-(96-94)(96+94)`
`=2.198+2.204-2.212-2.190`
`=2(198+204-212-190)`
`=2.0=0`
`⇒100^2 + 103^2 + 105^2 + 94^2 = 101^2 + 98^2 + 96^2 +107^2`
