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

Подмена x^(1/4) = t

t^2 - 2t = 0

t(t - 2) = 0

t = 0 или t - 2 = 0

t = 0, t = 2

Оборотная замена

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

x = 0^4, x = 2^4

x = 0, x = 16

Ответ: 16.