Решить уравнение: √x/2 + √2x/9 + √x/8=1/6

Имеем уравнение:

(x/2)^(1/2) + (2 * x)^(1/2)/9 + (x/8)^(1/2) = 1/6;

преобразуем левую часть равенства:

(x/2)^(1/2) + 1/3 * (4 * x/2)^(1/2) + (1/4 * x/2)^(1/2) = 1/6;

(x/2)^(1/2) + 2/3 * (x/2)^(1/2) + 1/2 * (x/2)^2 = 1/6;

(x/2)^(1/2) * (1 + 2/3 + 1/2) = 1/6;

(x/2)^(1/2) * (13/6) = 1/6;

(x/2)^(1/2) = 1/13;

x/2 = 1/169;

x = 2/169 - решение уравнения.