Найдите значение выражения x6y+xy6 / 5(3y-2x) * 2(2x-3y) / x5+y5 при x = 1/8 и y = -8.

Подставим значения x и y в выражение:

x = 1/8, y = -8

x^6y + xy^6 = (1/8)^6 * (-8) + (1/8) * (-8)^6 = -1/8^5 + 1/8 * 8^6 = -1/8^5 + 8^5

5(3y - 2x) = 5(3*(-8) - 2*(1/8)) = 5(-24 - 1/4) = 5(-97/4) = -485/4

x^5 + y^5 = (1/8)^5 + (-8)^5 = 1/8^5 - 8^5

2(2x - 3y) = 2(2*(1/8) - 3*(-8)) = 2(1/4 + 24) = 2(97/4) = 97/2

Выражение: (x^6y + xy^6) / (5(3y - 2x)) * (2(2x - 3y)) / (x^5 + y^5)

= (-1/8^5 + 8^5) / (-485/4) * (97/2) / (1/8^5 - 8^5)

= -(8^5 - 1/8^5) / (-485/4) * (97/2) / (1/8^5 - 8^5)

= (8^5 - 1/8^5) / (485/4) * (97/2) / -(8^5 - 1/8^5)

= - (97/2) / (485/4) = - (97/2) * (4/485) = - (97 * 2) / 485 = -194 / 485