Question

xin mọi người giải giúp em với ạ.em đang cần lắm!

Answer 1

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

\(A\ge\sqrt{\left(a+b+c\right)^2+\dfrac{1}{\left(a+b+c\right)^2}+\dfrac{80}{\left(a+b+c\right)^2}}\)

\(A\ge\sqrt{2\sqrt{\dfrac{\left(a+b+c\right)^2}{\left(a+b+c\right)^2}}+\dfrac{80}{1}}=\sqrt{82}\)

\(A_{min}=\sqrt{82}\) khi \(a=b=c=\dfrac{1}{3}\)