1. If a, B, C ∈ R +, a + B + C = 1, then the minimum value of A2 + B2 + C2 is_____________ 2. Let x, y ∈ R +, and X + 4Y = 4, find the maximum value of XY__________ 3. Let a = {(x, y) y ≥ 0.5 X-2}, B = {(x, y) y ≤ - x + B} a ∩ B ≠ & # 61638; (1) The value range of B is________ (2) If (x, y) ∈ a ∩ B, and the maximum value of X + 2Y is 9, then the value of B is_________ All three questions should be explained in detail,

1. If a, B, C ∈ R +, a + B + C = 1, then the minimum value of A2 + B2 + C2 is_____________ 2. Let x, y ∈ R +, and X + 4Y = 4, find the maximum value of XY__________ 3. Let a = {(x, y) y ≥ 0.5 X-2}, B = {(x, y) y ≤ - x + B} a ∩ B ≠ & # 61638; (1) The value range of B is________ (2) If (x, y) ∈ a ∩ B, and the maximum value of X + 2Y is 9, then the value of B is_________ All three questions should be explained in detail,

1. For real numbers a, B, C, there is a ^ 2 + B ^ 2 + C ^ 2 ≥ 1 / 3 * (a + B + C) ^ 2
2. For non negative real numbers a and B, there is a + B ≥ 2 √ (a * b) ≥ 0, that is, (a + b) / 2 ≥ √ (a * b) ≥ 0
Just assign the parameters