Question

ĐỀ : Cho \(M=\dfrac{54.107-53}{53.107-54}\); \(N=\dfrac{135.269-133}{134.269-135}\)

So sánh M vs N

Answer 1

\(M=\dfrac{54.107-53}{53.107-54}=\dfrac{53\left(107-1\right)+107}{53\left(107-1\right)-1}=\dfrac{53.106-1+108}{53.106-1}=1+\dfrac{108}{53.106-1}\)

\(N=\dfrac{135.269-133}{134.269-135}=\dfrac{134\left(269-1\right)-1+270}{134\left(269-1\right)-1}=1+\dfrac{270}{134.268-1}\)

\(M-N=\dfrac{108}{53.106-1}-\dfrac{270}{134.268-1}\)

\(M-N=\dfrac{2}{2.53^2-1}-\dfrac{5}{8.67^2-1}>\dfrac{5}{10.53^2-1}-\dfrac{5}{8.67^2-1}>0\)

M>N