a) \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^2-1\right)\left(3^2+1\right)...\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^{32}-1\right)< 3^{32}-1=B\)
b) \(A=2011.2013=\left(2012-1\right)\left(2012+1\right)=2012^2-1< 2012^2=B\)
b. (x + 4)2 - (x + 1)(x - 1) = 16
<=> (x + 4)2 - (x2 - 1) = 16
<=> x2 + 8x + 16 - x2 + 1 - 16 = 0
<=> 8x + 1 = 0
<=> 8x = -1
<=> x = \(\dfrac{-1}{8}\)
