Question

cho a + b + c =3

tìm cực trị

A = \(\sqrt{3a+bc}+\sqrt{3b+ac}+\sqrt{3c+ab}\)

Answer 1

Tìm cực trị là tim min hay max vậy bn? hay là cả 2? mk tìm max trước nha

\(A=\sqrt{a\left(a+b+c\right)+bc}+\sqrt{b\left(A+b+c\right)+ac}+\sqrt{c\left(a+b+c\right)+ab}\)

\(A=\sqrt{\left(a+b\right)\left(a+c\right)}+\sqrt{\left(a+b\right)\left(b+c\right)}+\sqrt{\left(a+c\right)\left(b+c\right)}\)

\(\Rightarrow A\le\frac{a+b+a+c}{2}+\frac{a+b+b+c}{2}+\frac{a+c+b+c}{2}=\frac{4\left(a+b+c\right)}{2}=6\)

Dấu "=" \(\Leftrightarrow a=b=c=1\)