Basic inequality: given a > 0, find the minimum value of A2 + 16 / A + A / A2 + 16 65 / 8 why do I calculate the minimum value of 2? And what's wrong with me?

Basic inequality: given a > 0, find the minimum value of A2 + 16 / A + A / A2 + 16 65 / 8 why do I calculate the minimum value of 2? And what's wrong with me?

(A2 + 16) / A + A / (A2 + 16) because (A2 + 16) / a = a + 16 / a ≥ 8, so (A2 + 16) / a = t, the original formula = t + 1 / T increases on [8, positive infinity], so the original formula min = 8 + 1 / 8 = 65 / 8. Your mistake is to use the inequality directly, ≥ 2, but this = holds if A2 + 16) / a = A / (A2 + 16), that is, a

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