JEE Advance - Mathematics (1982 - No. 39)
If $$a{x^2} + {b \over x} \ge c$$ for all positive $$x$$ where $$a>0$$ and $$b>0$$ show that $$27a{b^2} \ge 4{c^3}$$.
The inequality holds only if $$27ab^2 < 4c^3$$
The inequality holds only if $$27ab^2 = 4c^3$$
The inequality holds only if $$27ab^2 > 4c^3$$
The inequality holds only if $$27ab^2 \ge 4c^3$$
The inequality holds only if $$27ab^2 \le 4c^3$$