Question

Wiedząc że a+b=3 i a×b=1, oblicz a³+b³

Answer 1

Korzystamy ze wzoru:
(a+b)³ = a³ + 3a²b + 3ab² + b³

Mamy:
a³ + b³ = (a+b)³ - 3a²b - 3ab² = (a+b)³ - 3ab(a+b) = 3³ - 3 * 1 * 3 = 27 - 9 = 18

Answer 2

A³ + b³ = (a + b)(a² - ab + b²) = (a + b)[(a + b)² - 3ab] = 3[3² - 3 * 1] = 3(9 - 3) = 3 * 6 = 18