a)
9x² - 12x + 4 = 0
Zwijamy do kwadrtu różnicy: (a - b)² = a² - 2ab + b²
2ab = 12 /:2
ab = 6 ⇒ a = 3, b = 2, czyli:
(3x - 2)² = 0
3x - 2 = 0
3x = 2 /:3
x = 2/3
b)
25x² + 40x + 16 = 0
(a + b)² = a² + 2ab + b
2ab = 40 /:2
ab = 20 ⇒ a = 5, b = 4, czyli:
(5x + 4)² = 0
5x + 4 = 0
5x = -4 /:5
x = -4/5
c)
4x² - 28x + 49 = 0
2ab = 28 /:2
ab = 14 ⇒ a = 2, b = 7, czyli:
(2x - 7)² = 0
2x - 7 = 0
2x = 7 /:2
x = 7/2
x = 3¹/₂
