Question

So sánh x và y bằng cách nhanh nhất :

\(x=\frac{1989}{1990};y=\frac{2011}{2012}\)

Answer 1

Ta có:

\(x=\frac{1989}{1990}=1-\frac{1}{1990}\)

\(y=\frac{2011}{2012}=1-\frac{1}{2012}\)

Do \(\frac{1}{1990}>\frac{1}{2012}\)=> \(-\frac{1}{1990}< -\frac{1}{2012}\) => \(1-\frac{1}{1990}< 1-\frac{1}{2012}\)

=> \(x=\frac{1989}{1990}< y=\frac{2010}{2012}\)

Answer 2

Ta có :

x = \(\frac{1989}{1990}\)= 1 - \(\frac{1}{1990}\)

y = \(\frac{2011}{2012}\)= 1 - \(\frac{1}{2012}\)

Do \(\frac{1}{1990}\)> \(\frac{1}{2012}\)=> \(-\)\(\frac{1}{1990}\)< \(-\)\(\frac{1}{2012}\)=> \(1\)\(-\)\(\frac{1}{1990}\)\(< 1-\)\(\frac{1}{2012}\)

=> \(x\)\(=\)\(\frac{1989}{1990}\)\(< y=\)\(\frac{2010}{2012}\)