`a) y = (6x + 3)(5 - 2x)`
`-> 3(2x + 1)(5 - 2x) <= 3.((2x + 1 + 5 - 2x)/(2))^2`
`-> y <= 3.(6^2)/(2^2) = 27`
`text{Dấu}` "`=`"` text{xảy ra}`
`-> 2x + 1 = 5 - 2x`
`-> 4x = 4`
`-> x = 1`
`text{Vậy}` `y_{min} = 27` `text{khi}` `x = 1`
`b) y = (x^2)/((x^2 + 3)^3)`
`->` $y = \dfrac{1}{(\dfrac{x^2 + 2}{\sqrt[3]{x^2}})^3}$
`->` $y = \dfrac{1}{\dfrac{\sqrt[3]{x^6}}{\sqrt[3]{x^2}} + \dfrac{2}{\sqrt[3]{x^2}}}$
`->` $y = \dfrac{1}{\sqrt[3]{x^4} + \dfrac{1}{\sqrt[3]{x^2}} + \dfrac{1}{\sqrt[3]{x^2}}}$
`->` $y <= \dfrac{1}{3\sqrt[3]{\sqrt[3]{x^4}.\dfrac{1}{\sqrt[3]{x^2}}.\dfrac{1}{\sqrt[3]{x^2}}}}$
`-> y <= 1/27`
`text{Dấu}` "`=`"` text{xảy ra}`
$\sqrt[3]{x^2} = \dfrac{1}{\sqrt[3]{x^2}}$
`-> x^2 = 1`
`-> x = +-1`
`text{Vậy}` `y_{min} = 1/27` `text{khi}` `x = +-1`
