Question

A=98²⁰¹⁵+1/98²⁰¹⁴+1     voi    B=98²⁰¹⁴+1/98²⁰¹³+1

so sánh A và B

Answer 1

\(A=\frac{98^{2015}+1}{98^{2014}+1}>1\)

Ta có:

\(A=\frac{98^{2015}+1+97}{98^{2014}+1+97}=\frac{98^{2015}+98}{98^{2014}+98}=\frac{98\left(98^{2014}+1\right)}{98\left(98^{2013}+1\right)}\)

\(=\frac{98\left(98^{2015}+1\right)}{98\left(98^{2014}+1\right)}=\frac{98^{2014}+1}{98^{2013}+1}\)

Ta thấy: \(\frac{98^{2014}+1}{98^{2013}+1}=B\)mà \(A>1\)

\(\Rightarrow A>B\)

Answer 2

\(A=\frac{98^{2015}+1}{98^{2014}+1}>1\)

Theo đề ta có:

\(A=\frac{98^{2015}+1+97}{98^{2014}+1+97}=\frac{98^{2015}+98}{98^{2014}+98}=\frac{98\left(98^{2014}+1\right)}{98\left(98^{2013}+1\right)}\) 

   \(=\frac{98\left(98^{2015}+1\right)}{98\left(98^{2014}+1\right)}=\frac{98^{2014}+1}{98^{2013}+1}\)

Lúc này ta thấy: \(\frac{98^{2014}+1}{98^{2013}+1}=B\)mà  \(A>1\)

\(\Leftrightarrow A>B\).