Prove for all a and b the inequalities: a) a² + b² ≥ 2ab b) (c²a²)/2 + (b²)/(2c²

Prove for all a and b the inequalities: a) a² + b² ≥ 2ab b) (c²a²)/2 + (b²)/(2c²) ≥ ab (c is any nonzero number) c) (a² + b²)/2 ≥ ((a + b)/2)² d) (a + b)/2 ≥ 2 / (1/a + 1/b) (for a, b >