The sides of a triangle are \(a\), \(b\), \(c\), and \(s\) is given by \(2s = a + b + c\).

Prove that

- \(4(s-b)(s-c) \le a^2\),
- \(8(s-a)(s-b)(s-c) \le abc\).

State under what conditions the sign of equality applies, in each case.

Investigate the truth of the results (i) and (ii) if \(a\), \(b\), \(c\) are *any* positive quantities, not necessarily the sides of a triangle.