Question

Answer 1

\(A=\dfrac{\sqrt{ab+c\left(a+b+c\right)}+\sqrt{2\left(a^2+b^2\right)}}{3+\sqrt{ab}}=\dfrac{\sqrt{\left(a+c\right)\left(b+c\right)}+\sqrt{2\left(a^2+b^2\right)}}{3+\sqrt{ab}}\)

\(A\ge\dfrac{\sqrt{\left(\sqrt{ab}+c\right)^2}+\sqrt{\left(a+b\right)^2}}{3+\sqrt{ab}}=\dfrac{\sqrt{ab}+c+a+b}{3+\sqrt{ab}}=\dfrac{\sqrt{ab}+3}{3+\sqrt{ab}}=1\)

\(A_{min}=1\) khi \(a=b\)