Observe the following formulas: 50 × 50 = 50 ^ 2-0 ^ 2 = 2500 49 × 51 = 50 ^ 2-1 ^ = 2499 48 × 52 = 50 ^ 2-2 ^ 2 = 2496 According to the above rule, if a + B = 200 (a, B are positive), what is the maximum value of AB

Observe the following formulas: 50 × 50 = 50 ^ 2-0 ^ 2 = 2500 49 × 51 = 50 ^ 2-1 ^ = 2499 48 × 52 = 50 ^ 2-2 ^ 2 = 2496 According to the above rule, if a + B = 200 (a, B are positive), what is the maximum value of AB

50×50=50^2-0^2=2500
49×51=50^2-1^=2499
48×52=50^2-2^2=2496
obviously
When a = B, AB has a maximum
a+b=200
a+a=200
a=b=100
AB max = 100 × 100 = 10000