Explanation

For statement 1, divide both sides by (a − b) > 0: it becomes (a+b)/(a²+b²) > 1/(a+b), i.e. (a+b)² > a² + b², i.e. 2ab > 0, which is true. For statement 2, cross-multiplying (all terms positive) gives (a³+b³)(a+b) − (a²+b²)² = ab(a−b)², which is positive whenever a ≠ b — not only when a > b > 0, so the 'only when' clause makes the statement false. Hence 1 only is correct, option (a).