∵ b = √（a ² - 9）+ √（9 - a ²）+ 91
∴ a ² - 9 ≥ 0
9 - a ² ≥ 0
∴ a ² ≥ 9 ,a ² ≤ 9
∴ a ² = 9
a = ± 3
∵ a > 0
∴ a = 3
∴ b = √0 + √0 + 91 = 91
当 a = 3 时,则：a ³ - b = 3 ³ - 91 = 27 - 91 = - 64
∴ a ³ - b 的立方根 = ³ √（a ³ - b）= ³√（- 64）= - 4