Question

Cho 3 số dương \(a,b,c\) và \(a+b+c=1\)

CMR \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\ge9\)

Answer 1

-Áp dụng BĐT Caushy Schwarz ta có:

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

-Dấu "=" xảy ra khi \(a=b=c=\dfrac{1}{3}\)