Question

[Trần Thu Linh]

cho a,b,c thuộc Q thỏa mãn a+2b+3c>=20. Tím GTNN: a+b+c+3/a+9/2b+4/c

Answer 1

[Mr Lazy]

\(A=\left(\frac{3}{a}+\frac{3a}{4}\right)+\left(\frac{9}{2b}+\frac{b}{2}\right)+\left(\frac{4}{c}+\frac{c}{4}\right)+\frac{1}{4}\left(a+2b+3c\right)\)

\(\ge2\sqrt{\frac{3}{a}.\frac{3a}{4}}+2\sqrt{\frac{9}{2b}.\frac{b}{2}}+2\sqrt{\frac{4}{c}.\frac{c}{4}}+\frac{1}{4}.20\)

\(=3+3+2+5\)

\(=13\)

Dấu "=" xảy ra khi \(a=2;\text{ }b=3;\text{ }c=4\)

Vậy GTNN của A là 13.