lean_workbook_plus_4999

Let $a,b > 0$ . Prove that: $\left( {{a^2} + b + \frac{3}{4}} \right)\left( {{b^2} + a + \frac{3}{4}} \right) \ge \left( {2a + \frac{1}{2}} \right)\left( {2b + \frac{1}{2}} \right)$