Question

cho A=10^2014+1/10^2015+1 và B=10^2015+1/10^2016+1. So sánh A và B            

nhớ ghi luôn cách giải nghen

Answer 1

Ta có: \(10A=10.\left(\frac{10^{2014}+1}{10^{2015}+1}\right)=\frac{10^{2015}+10}{10^{2015}+1}=\frac{10^{2015}+1+9}{10^{2015}+1}=1+\frac{9}{10^{2015}+1}\)

\(10B=10.\left(\frac{10^{2015}+1}{10^{2016}+1}\right)=\frac{10^{2016}+10}{10^{2016}+1}=\frac{10^{2016}+1+9}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)

Vì 1 = 1; 9 = 9 ta so sánh mẫu:

Ta có: 10²⁰¹⁵ < 10²⁰¹⁶ => 10²⁰¹⁵+1 < 10²⁰¹⁶+1

=> \(1+\frac{9}{10^{2015}+1}>1+\frac{9}{10^{2016}+1}\)

=> 10A > 10B

=> A > B.