Bạn tham khảo
Áp dụng BĐT AM-GM cho các cặp số sau ( $\dfrac{1}{a};$ $\dfrac{1}{b})$
$\dfrac{1}{a}+$ $\dfrac{1}{b}≥$ $\dfrac{2}{\sqrt{ab}}$
Tương quan tự ta được
$\dfrac{1}{a}+$ $\dfrac{1}{c}≥$ $\dfrac{2}{\sqrt{ac}}$
$\dfrac{1}{b}+$ $\dfrac{1}{c}≥$ $\dfrac{2}{\sqrt{bc}}$
⇒$2(\dfrac{1}{a}+$ $\dfrac{1}{b}+$$\dfrac{1}{c})≥$$\dfrac{2}{\sqrt{ab}}+$ $\dfrac{2}{\sqrt{ac}}+$ $\dfrac{2}{\sqrt{bc}}$
⇒$\dfrac{1}{a}+$ $\dfrac{1}{b}+$$\dfrac{1}{c}≥$$\dfrac{1}{\sqrt{ab}}+$ $\dfrac{1}{\sqrt{ac}}+$ $\dfrac{1}{\sqrt{bc}}$
Học tốt
