Question 149
(1) Prove $t^3 \geq t^2 + 4$ for $t \geq 2$, and find the condition under which equality holds.
(2) For any numbers $t_1, t_2, \ldots, t_n \geq 2$, prove that
$$
\frac{t_1^3}{t_2^2 + 4} + \frac{t_2^3}{t_3^2 + 4} + \dots + \frac{t_{n-1}^3}{t_n^2 + 4} + \frac{t_n^3}{t_1^2 + 4} \geq n,
$$
and find the condition under which equality holds.
(2) For any numbers $t_1, t_2, \ldots, t_n \geq 2$, prove that
$$
\frac{t_1^3}{t_2^2 + 4} + \frac{t_2^3}{t_3^2 + 4} + \dots + \frac{t_{n-1}^3}{t_n^2 + 4} + \frac{t_n^3}{t_1^2 + 4} \geq n,
$$
and find the condition under which equality holds.