Odpowiedź:
xy = 2
x = 2/y
(x + 1)(y + 2) ≥ 8
(2/y + 1)(y + 2) ≥ 8
2 + y + 4/y + 2 ≥ 8
4 + y + 4/y = ≥ 8 | * y
4y + y² + 4 ≥ 8y
y² + 4y - 8y + 4 ≥ 0
y² - 4y + 4 ≥ 0
a = 1 , b = - 4 , c = 4
Δ = b² - 4ac = (-4)² - 4 * 1 * 4 = 16 - 16 = 0
y = - b/2a = 4/2 = 2
xy = 2
x * 2 = 2
2x = 2
x = 2/2 = 1
(x + 1)(y + 2) ≥ 8
(1 + 1)(2 + 2) ≥ 8
2 * 4 ≥ 8
8 ≥ 8
