Question

so sánh \(\frac{-1}{\sqrt{33}-\sqrt{31}}\) và \(\frac{-1}{\sqrt{34}-\sqrt{32}}\)

Answer 1

+ \(-\frac{1}{\sqrt{33}-\sqrt{31}}=-\frac{\sqrt{33}+\sqrt{31}}{\left(\sqrt{33}-\sqrt{31}\right)\left(\sqrt{33}+\sqrt{31}\right)}\)

\(=-\frac{\sqrt{33}+\sqrt{31}}{2}\)

+ \(-\frac{1}{\sqrt{34}-\sqrt{32}}=-\frac{\sqrt{34}+\sqrt{32}}{2}\)

+ \(\sqrt{34}+\sqrt{32}>\sqrt{33}+\sqrt{31}\)

\(\Rightarrow-\left(\sqrt{34}+\sqrt{32}\right)< -\left(\sqrt{33}+\sqrt{31}\right)\)

\(\Rightarrow-\frac{\sqrt{33}+\sqrt{31}}{2}>-\frac{\sqrt{34}+\sqrt{32}}{2}\)

\(\Rightarrow-\frac{1}{\sqrt{33}-\sqrt{31}}>-\frac{1}{\sqrt{34}-\sqrt{32}}\)