Question

C) (4√5+√3)(4√5-√3)
d)(√8+2√6)(2√6-√8)
e)(√6-3√3)²
f)(2√32-3√2)²

Answer 1

Skorzystam ze wzorów:
(a-b)*(a+b) = a² - b² (zad. c, d)
(a-b)² = a² - 2ab + b² (zad. e)

c) (4√5+√3)*(4√5-√3) = (4√5)² - √3² = 16*5 - 3 = 80 - 3 = 77
d) (2√6+√8)*(2√6-√8) = (2√6)² - √8² = 4*6 - 8 = 24 - 8 = 16
e) (√6 - 3√3)² = √6² - 2*√6*3√3 + (3√3)² = 6 + 6√18 + 9*3
   = 6 + 6*(3√2) + 27 = 33 + 18√2
f) (2√32 - 3√2)² = (2*(4√2) - 3√2)² = (8√2 - 3√2)² = (5√2)² = 25*2 = 50.