Odpowiedź:
Szczegółowe wyjaśnienie:
Ćw. 7
a) (5 - √7)(5 + √7) = [wzór skróconego mnożenia (a - b)(a + b) = a² - b²]
to
= 5² - (√7)² = 25 - 7 = 18
b)
(√5 + 1)( 1 - √5) = - (√5 + 1)(√5 - 1) = - (√5² - 1²) = - (5 - 1) = - 4
c)
(1/3 - √6/2)(1/3 + √6/2) = (1/3)² - (√6/2)² = 1/9 - 6/4 = 1/9 - 3/2 =
2/18 - 27/18 = - 25/18 = - 18/18 - 7/18 = - 1 - 7/18 = - 1 7/18
d)
(2√2 - 3)(3 + 2√2) = - (3 - 2√2)(3 + 2√2) = - (9 - 8) = - 1
e)
(√2 - √3)(√2 + √3) = 2 - 3 = - 1
f)
(√5 - √2/2)(√5 + √2/2) = 5 - 2/4 = 5 - 1/2 = 4½
