Ta có a+b+c+2\sqrt{ac+bc}=c+(a+b)+2\sqrt{c(a+b)}=(\sqrt{c}+\sqrt{a+b})^{2}Tương tự: a+b+c-2\sqrt{ac+bc}=(\sqrt{c}-\sqrt{a+b})^{2}$\rightarrow A=\sqrt{a+b+c+2\sqrt{ac+bc} } + \sqrt{a+b+c-2\sqrt{ac+bc}}=\sqrt{c}+\sqrt{a+b}+\left| {\sqrt{c}-\sqrt{a+b}} \right|*Nếu c>a+b thì A=2\sqrt{c}*Nếu c<a+b thì A=2\sqrt{a+b}
Ta có
a+b+c+2\sqrt{ac+bc}=c+(a+b)+2\sqrt{c(a+b)}=(\sqrt{c}+\sqrt{a+b})^{2}Tương tự:
a+b+c-2\sqrt{ac+bc}=(\sqrt{c}-\sqrt{a+b})^{2}$\rightarrow A=
\sqrt{a+b+c+2\sqrt{ac+bc}}+\sqrt{a+b+c-2\sqrt{ac+bc}}=\sqrt{c}+\sqrt{a+b}+\left| {\sqrt{c}-\sqrt{a+b}} \right|
*Nếu c>a+b
thì A=2\sqrt{c}
$*Nếu
c<a+b thì
A=2\sqrt{a+b}