Question

Bài 1:So sánh hai số:

a)A=2015^2 và B=2014.2016

b)C=3^16-1 và D=8(3^2+1)(3^4+1)(3^8+1)

Answer 1

\(a.A=2015^2=2015\left(2014+1\right)=2015.2014+2015\)

\(B=2014.2016=2014.\left(2015+1\right)=2015.2014+2014\)

Vì \(2015>2014\Rightarrow2015.2014+2015>2015.2014+2014\)

\(\Rightarrow A>B\)

\(b.C=3^{16}-1\)

\(D=8.\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right)\)

\(=\left(3^4-1\right).\left(3^4+1\right).\left(3^8+1\right)=\left(3^8-1\right)\left(3^8+1\right)=3^{16}-1\)

Vì \(3^{16}-1=3^{16}-1\Rightarrow C=D\)