Given that a and B are natural numbers and a + B = 40, find the minimum of (1) a + B and the maximum of (2) ab emergency I hope 99% of them are right

Given that a and B are natural numbers and a + B = 40, find the minimum of (1) a + B and the maximum of (2) ab emergency I hope 99% of them are right

(1) Suppose a and B are positive natural numbers, then a + B ≥ 2Ab, 2 (a + b) ≥ 40 * 40 = 1600 when equal, so the minimum value of a + B is 1600 △ 2 = 800
(2) The maximum value of AB is in the case that a and B are positive natural numbers, a + B = 40 ≥ 2 √ AB, so the minimum value is 20 * 20 = 400

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