Question

so sánh :a)A=2015.2017 va B=2016^2

b)C=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1) va D=2^32

Answer 1

a ) \(A=2015.2017=\left(2016-1\right)\left(2016+1\right)=2016^2-1\)

Do \(2016^2>2016^2-1\)

\(\Rightarrow B>A\)

b ) \(C=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1< 2^{32}=D\)

Vậy \(C< D\)

Answer 2

so sánh :a)A=2015.2017 va B=2016²

Ta có: A = 2015.2017 = (2016-1)(2016+1)

= 2016²-1<2016²

=> A < B