1.
(x-4).(xy+1)=11
=> (x-4).(xy+1) ∈ Ư(11)={±1 ; ±11}
TH1 : x-4=1 -> x=5
xy +1=1 -> 5y + 1=1 ->5y=0 ->y=0
TH2 : x-4=-1 -> x=3
xy+1=-1 -> 3y+1=-1 ->3y=-2 ->-2/3
TH3 : x-4=11 ->x=15
xy + 1=11 ->15y+1=11 ->15y=10 ->2/3
TH4 : x-4=-11 ->x=-7
xy+1=-11 ->-7y+1=-11 ->-7y=-12 ->y=12/7
2.
B=1-2+2^2-2^3+2^4-2^5+...+2^2008
2B=2( 1-2+2^2-2^3+2^4-2^5+...+2^2008)
2B= 2-2² + 2³-2^4 + ....+2^2009
2B-B =(2-2² + 2³-2^4 + ....+2^2009) - (1-2+2^2-2^3+2^4-2^5+...+2^2008 )
B=(2-2)+(2²-2²)+...+(2^2008 - 2^2008) + (2^2009 -1)
B=0+0+...+0+2^2009 -1
B=2^2009 -1
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