The basic inequality of Mathematics 1. If x > 1, Y > 1 and lgx + lgY = 4, then the maximum value of lgx * lgY is A.4 B.2 C.1 D.1/4 2. It is known that P > 0, Q > 0, and the median of P and Q is 1 / 2. If x = P + 1 / P, y = q + 1 / Q, then the minimum value of X + y is a.3b.4c.5d.6 3. Given a ≥ - 1 / 2, B ≥ - 1 / 2, and a + B = 1, then the maximum value of √ (2a + 1) + √ (2B + 1) is_______

The basic inequality of Mathematics 1. If x > 1, Y > 1 and lgx + lgY = 4, then the maximum value of lgx * lgY is A.4 B.2 C.1 D.1/4 2. It is known that P > 0, Q > 0, and the median of P and Q is 1 / 2. If x = P + 1 / P, y = q + 1 / Q, then the minimum value of X + y is a.3b.4c.5d.6 3. Given a ≥ - 1 / 2, B ≥ - 1 / 2, and a + B = 1, then the maximum value of √ (2a + 1) + √ (2B + 1) is_______

Lgx + lgY = 4 ≥ 2sqrt (lgx * lgY) select b
p+q=1≥2Sqrt(pq)
pq≤1/4
X + y = 1 + 1 / P + 1 / Q = 1 + 1 / PQ ≥ 1 + 4 = 5 choose C
The results show that [√ (2a + 1) + √ (2B + 1)] / 2 ≤ sqrt [(2a + 1 + 2B + 1) / 2] = 2, weighted greater than arithmetic
√(2a+1)+√(2b+1)≤4