Question

Chứng minh bất đẳng thức 

\(\frac{12}{\sqrt{13}}+\frac{13}{\sqrt{12}}>\sqrt{12}+\sqrt{13}\)

Answer 1

Ta có:

\(\frac{12}{\sqrt{13}}+\frac{13}{\sqrt{12}}=\frac{12\sqrt{13}}{13}+\frac{13\sqrt{12}}{12}=\frac{13\sqrt{13}-\sqrt{13}}{13}+\frac{12\sqrt{12}+\sqrt{12}}{12}\)\(=\sqrt{12}+\sqrt{13}+\frac{1}{\sqrt{12}}-\frac{1}{\sqrt{13}}>\sqrt{12}+\sqrt{13}\)