Question

Answer 1

17.

-Áp dụng BĐT Caushy Schwarz ta có:

\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\ge\dfrac{\left(1+1+1\right)^2}{a+b+c}\ge\dfrac{9}{\dfrac{3}{2}}=6\)

-Dấu bằng xảy ra \(\Leftrightarrow a=b=c=\dfrac{1}{2}\)

Answer 2

\(a+b+c+\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\left(a+\dfrac{1}{4a}\right)+\left(b+\dfrac{1}{4b}\right)+\left(c+\dfrac{1}{4c}\right)+\dfrac{3}{4}\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)\ge1+1+1+\dfrac{3}{4}.6=\dfrac{15}{2}\)-Dấu bằng xảy ra \(\Leftrightarrow a=b=c=\dfrac{1}{2}\)