Question

[Incursion_03]

Cho \(0\le x;y;z\le2\)và x + y + z = 5. Tìm \(A_{min}=\sqrt{x}+\sqrt{y}+\sqrt{z}\)

Answer 1

[tthnew]

Nếu là tìm max thì làm như sau:

\(A=\sqrt{\dfrac{3}{5}}.\left(\sqrt{\dfrac{5}{3}.x}+\sqrt{\dfrac{5}{3}.y}+\sqrt{\dfrac{5}{3}.z}\right)\)

\(\le\sqrt{\dfrac{3}{5}}.\left(\dfrac{x+y+z+5}{2}\right)=\sqrt{\dfrac{3}{5}}.5=\sqrt{15}\)

Dấu "=" xảy ra khi \(x=y=z=\dfrac{5}{3}\)

Answer 2

[tthnew]

Đề phải là tìm max chứ?