Comparison of a math problem in Senior Two If a > 0, b > 0, then the relation between the power of (a + b) / 2 of P = (AB) and q = a ^ b * B ^ A is

Comparison of a math problem in Senior Two If a > 0, b > 0, then the relation between the power of (a + b) / 2 of P = (AB) and q = a ^ b * B ^ A is

P / Q is reduced to (a-b) / 2 power of (A / b)
When B ≥ a, 0b, a / b > 1 (a-b) / 2 > 0, the above formula > 1 p > q is discussed
In conclusion, P ≥ Q