Problem

Source: 2019 Romania JBMO TST 5.2

Tags: algebra, inequalities



Let $a, b, c, d \ge 0$ such that $a^2 + b^2 + c^2 + d^2 = 4$. Prove that $$\frac{a + b + c + d}{2} \ge 1 + \sqrt{abcd}$$When does the equality hold? Leonard Giugiuc and Valmir B. Krasniqi