Looking at the inequality, [MATH]\sqrt{x+3} + \sqrt[4]{9-x} > \sqrt{3}[/MATH], we can consider two cases. If x > 0, the first term alone is greater than the RHS, and the second is positive (unless x = 9), so the inequality is true. On the other hand, if x < 0, the second term alone is greater than the RHS, and the first is positive (unless x = -3), so again it is true.