Ta có:
$\left ( x-\frac{3}{2} \right )\left ( x-\frac{1}{2} \right )\left ( x+\frac{1}{2} \right )\left ( x+\frac{3}{2} \right )= \left ( x^{2}-\frac{9}{4} \right )\left ( x^{2}-\frac{1}{4} \right )= \left ( x^{2}-\frac{1}{4} \right )^{2}-2\left ( x^{2}-\frac{1}{4} \right )+1-1= \left ( x^2-\frac{1}{4}-1 \right )^{2}-1= \left ( x^2-\frac{5}{4} \right )^{2}-1\geq -1$
Suy ra:
Min $\left ( x+27 \right )\left ( x+28 \right )\left ( x+29 \right )\left ( x+30 \right )= -1$
Suy ra:
Min $\left ( x+27 \right )\left ( x+28 \right )\left ( x+29 \right )\left ( x+30 \right) +27282930 \doteq 27282930-1\doteq 27282929$