Question

Пусть x1 и x2- корни уравнения 3x²+8x-1=0. Не решая уравнения, найдите x1x2³ и x2x1³

Answer 1

Ответ:

8 и -2 целых 16/27.

Объяснение:

x1 + x2 = -b/a = -8/3

x1x2 = c/a = -1/3

1/x1 + 1/x2 = (x1+x2) / x1x2 = -8/3 : (-1/3) = 8/3 * 3 = 8

x1x2³ + x2x1³ = x1x2(x1²+x2²) = x1x2(x1²+2x1x2+x2²-2x1x2) = x1x2 * ((x1+x2)²-2x1x2) = -1/3* ((-8/3)² - 2*(-1/3)) = -1/3* (64/9 + 2/3) = -70/27 = -2 целых 16/27