Nguyễn Bùi Đại Hiệp phục bạn này lần nào hỏi cũng chép sai đề.
\(a+b+c+\sqrt{abc}=4\)
\(\Leftrightarrow4\left(a+b+c\right)+4\sqrt{abc}=16\)(*)
\(A=\Sigma\left(\sqrt{a\left(4-b\right)\left(4-c\right)}\right)-\sqrt{abc}\)
\(A=\Sigma\left(\sqrt{a\left(16-4b-4c+bc\right)}\right)-\sqrt{abc}\)
Thay (*) vào A ta được :
\(A=\Sigma\left(\sqrt{a\left(4a+4b+4c+4\sqrt{abc}-4b-4c+bc\right)}\right)-\sqrt{abc}\)
\(A=\Sigma\left(\sqrt{a\left(4a+4\sqrt{abc}+bc\right)}\right)-\sqrt{abc}\)
\(A=\Sigma\sqrt{a\left(2\sqrt{a}+\sqrt{bc}\right)^2}-\sqrt{abc}\)
\(A=\Sigma\left[\sqrt{a}\cdot\left(2\sqrt{a}+\sqrt{bc}\right)\right]-\sqrt{abc}\)
\(A=\Sigma\left(2a+\sqrt{abc}\right)-\sqrt{abc}\)
\(A=2\left(a+b+c\right)+3\sqrt{abc}-\sqrt{abc}\)
\(A=2\left(a+b+c\right)+2\sqrt{abc}\)
\(A=2\left(a+b+c+\sqrt{abc}\right)\)
\(A=2\cdot4=8\)
Vậy....