chỉ cần làm câu 3,4,5,6
3.
\(D=2\left(x^2+4\right)+\left(y^2+1\right)+\dfrac{28}{x}+\dfrac{1}{y}-9\)
\(D\ge8x+2y+\dfrac{28}{x}+\dfrac{1}{y}-9\)
\(D\ge7\left(x+\dfrac{4}{x}\right)+\left(y+\dfrac{1}{y}\right)+x+y-9\)
\(D\ge14\sqrt{\dfrac{4x}{4}}+2\sqrt{\dfrac{y}{y}}+3-9=24\)
\(D_{min}=24\) khi \(\left(x;y\right)=\left(2;1\right)\)
5.
\(P=12\left(x+\dfrac{4}{x}\right)+24\left(y+\dfrac{9}{y}\right)+16\left(z+\dfrac{16}{z}\right)-\left(6x+4y+3z\right)\)
\(P\ge24\sqrt{\dfrac{4x}{x}}+48\sqrt{\dfrac{9y}{y}}+32\sqrt{\dfrac{16z}{z}}-36\)
\(P\ge444\)
\(P_{min}=444\) khi \(\left(x;y;z\right)=\left(2;3;4\right)\)
Bài 4 và 6 trùng nhau?
\(A=\left(\dfrac{3x}{4}+\dfrac{3}{x}\right)+\left(\dfrac{y}{2}+\dfrac{9}{2y}\right)+\left(\dfrac{z}{4}+\dfrac{4}{z}\right)+\dfrac{1}{4}\left(x+2y+3z\right)\)
\(A\ge2\sqrt{\dfrac{9x}{4x}}+2\sqrt{\dfrac{9y}{4y}}+2\sqrt{\dfrac{4z}{4z}}+\dfrac{1}{4}.20\)
\(A\ge13\)
\(A_{min}=13\) khi \(\left(x;y;z\right)=\left(2;3;4\right)\)
