1 / (x^ (1/4) - 1) + 3 / (x^ (1/4) + 1) = 2 найти наибольший корень уравнения

Приведем к общему знаменателю:

(x^ (1/4) + 1 + 3 (x^ (1/4) - 1)) / ((x^ (1/4) - 1) (x^ (1/4) + 1)) = 2

(x^ (1/4) + 1 + 3x^ (1/4) - 3) / ((x^ (1/4)) ^2 - 1^2) = 2

(4x^ (1/4) - 2) / (x^ (1/2) - 1) = 2/1

4x^ (1/4) - 2 = 2 (x^ (1/2) - 1)

4x^ (1/4) - 2 = 2x^ (1/2) - 2

4x^ (1/4) - 2 - 2x^ (1/2) + 2 = 0

4x^ (1/4) - 2x^ (1/2) = 0 | : (-2)

x^ (1/2) - 2x^ (1/4) = 0

Замена x^ (1/4) = t

t^2 - 2t = 0

t (t - 2) = 0

t = 0 или t - 2 = 0

t = 0, t = 2

Обратная замена

x^ (1/4) = 0, x^ (1/4) = 2

x = 0^4, x = 2^4

x = 0, x = 16

Ответ: 16.