If a = a ^ 2 + 5B ^ 2-4ab + 2B + 2009, find the minimum value of a!

If a = a ^ 2 + 5B ^ 2-4ab + 2B + 2009, find the minimum value of a!

Given a ＞ B ＞ 0, find the minimum value of a 2 + 16b (a − b)

∵ B (a-b) ≤ (B + a − B2) 2 = A24, ∵ A2 + 16b (a − b) ≥ A2 + 64a2 ≥ 16. If and only if B = a − Ba2 = 8, i.e. a = 22b = 2, the equal sign is taken

Let a > b > 0, find the minimum value of A2 + 16 / (b (a-b))

Then B (a-b) ≤ [(B + a-b) / 2] ^ 2 = a ^ 2 / 4 (if and only if B = A-B = A / 2, take the equal sign), so 16 / b (a-b) ≥ 16 / (a ^ 2 / 4) = 64 / A ^ 2, then a ^ 2 + 16 / b (a-b) ≥ a ^ 2 + 64 / A ^ 2 ≥ 2 * root sign (a ^ 2 * 64 / A ^ 2) = 16 (if and only if a ^