Đáp án:
`a)A=-1`
`b)B=5^128-3^128`
Giải thích các bước giải:
`a)A=(2+1)(2²+1)(2^4+1)...(2^32+1)-2^64`
`=1.(2+1)(2²+1)(2^4+1)...(2^32+1)-2^64`
`=(2-1)(2+1)(2²+1)(2^4+1)...(2^32+1)-2^64`
`=(2²-1)(2²+1)(2^4+1)...(2^32+1)-2^64`
`=[(2^2)^2-1^2](2^4+1)...(2^32+1)-2^64`
`=(2^4-1)(2^4+1)...(2^32+1)-2^64`
`=[(2^4)^2-1^2]...(2^32+1)-2^64`
`=(2^8-1)...(2^32+1)-2^64`
`=(2^32-1)(2^32+1)-2^64`
`=(2^32)^2-1^2-2^64`
`=2^64-1-2^64`
`=-1`
`b)B=(5+3)(5²+3²)(5^4+3^4)...(5^64+3^64)+(5^128-3^128)/2`
`=[2(5+3)(5²+3²)(5^4+3^4)...(5^64+3^64)]/2+(5^128-3^128)/2`
`=[2(5+3)(5²+3²)(5^4+3^4)...(5^64+3^64)+5^128-3^128)/2`
`=[(5-3)(5+3)(5²+3²)(5^4+3^4)...(5^64+3^64)+5^128-3^128)/2`
`=[(5^2-3^2)(5²+3²)(5^4+3^4)...(5^64+3^64)+5^128-3^128)/2`
`=[[(5^2)^2-(3^2)^2](5^4+3^4)...(5^64+3^64)+5^128-3^128)/2`
`=[(5^4-3^4)(5^4+3^4)...(5^64+3^64)+5^128-3^128)/2`
`=[[(5^4)^2-(3^4)^2]...(5^64+3^64)+5^128-3^128)/2`
`=[(5^8-3^8)...(5^64+3^64)+5^128-3^128)/2`
`=[(5^64-3^64)(5^64+3^64)+5^128-3^128)/2`
`=[(5^64)^2-(3^64)^2+5^128-3^128)/2`
`=[5^128-3^128+5^128-3^128)/2`
`=[2(5^128-3^128)]/2`
`=5^128-3^128`
