Question

Không quy đồng mẫu số hãy so sánh:

A=-9/10²⁰¹⁰+-19/10²⁰¹¹; B=-9/10²⁰¹¹+-19/10²⁰¹⁰

 

Answer 1

\(A=-\frac{9}{10^{2010}}-\frac{19}{10^{2011}}=-\frac{9}{10^{2010}}-\frac{10}{10^{2010}}+\frac{10}{10^{2010}}-\frac{9}{10^{2011}}-\frac{10}{10^{2011}}.\)

\(=-\frac{19}{10^{2010}}-\frac{9}{10^{2011}}+\frac{1}{10^{2009}}-\frac{1}{10^{2010}}=B+\frac{1}{10^{2009}}-\frac{1}{10^{2010}}\)

\(\Rightarrow A-B=\frac{1}{10^{2009}}-\frac{1}{10^{2010}}>0\Rightarrow A>B.\)

Answer 2

\(-A=\frac{9}{10^{2010}}+\frac{19}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{10}{10^{2011}}+\frac{9}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{1}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{10}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{1}{10^{2009}}+\frac{9}{10^{2011}}\)

Tương tự với B, ta có:

\(-B=\frac{9}{10^{2011}}+\frac{19}{10^{2010}}\)

\(-B=\frac{9}{10^{2011}}+\frac{10}{10^{2010}}+\frac{9}{10^{2010}}\)

\(-B=\frac{9}{10^{2010}}+\frac{1}{10^{2009}}+\frac{9}{10^{2010}}\)

Ta thấy -B > -A \(\Rightarrow\)A > B.

Answer 3

A=\(\frac{-9}{10^{2011}^{ }}\)+\(\frac{-19}{10^{2011}}\)=\(\frac{-9}{10^{2010}}\)+\(\frac{-9}{10^{2011}}\)+\(\frac{-10}{2011}\)

B=\(\frac{-9}{10^{2011}}\)+\(\frac{-19}{10^{2010}}\)=\(\frac{-9}{10^{2011}}\)+\(\frac{-9}{10^{2010}}\)+\(\frac{-10}{2010}\) \(\frac{-10}{2011}\)>\(\frac{-10}{2010}\)vậy A>B