Vì [tex](3x-2y)^2\geq 0,(x^3y-24)^4\geq 0\Rightarrow (3x-2y)^2+(x^3y-24)^4\geq 0[/tex]
Dấu "=" xảy ra khi [tex]\left\{\begin{matrix} 3x=2y\\ x^3y=24 \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=\frac{2}{3}y\\ x^3y=24 \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=\frac{2}{3}y\\ y^4.\frac{8}{27}=24 \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=\frac{2}{3}y\\ y=\pm 3 \end{matrix}\right.[/tex]
+ y=3 => x=2
+ y=-3 => x=-2