Question

(√a-√b)/(a^(1/4)-b^(1/4) ) Срочно . помогите решить.

Answer 1

Answer 2

Для упрощения выражения можно использовать формулу a^2 - b^2 = (a-b)(a+b):

(√a-√b)/(a^(1/4)-b^(1/4) ) = ((√a-√b)(a^(1/4)+b^(1/4)))/((a^(1/4)-b^(1/4))(a^(1/4)+b^(1/4))) = ((√a-√b)(a^(1/4)+b^(1/4)))/(a^(1/2)-b^(1/2))

Теперь можно умножить числитель и знаменатель на (a^(1/4)+b^(1/4)):

((√a-√b)(a^(1/4)+b^(1/4)))/(a^(1/2)-b^(1/2)) = ((a-b)(a^(1/4)-b^(1/4)))/(a^(1/2)-b^(1/2))(a^(1/4)+b^(1/4)) = (a-b)/(a^(1/2)+b^(1/2))

Ответ: (a-b)/(a^(1/2)+b^(1/2))