Question

Решите уравнение

$frac{x}{5} + frac{1}{x} =4$

Answer 1

x/5 + 1/x = 4

x != 0 - ОДЗ

(x^2)/5 + 1 = 4x

x^2 - 20x + 5 = 1

x1,2 = (20 +- sqrt(400 - 20))/2

x1,2 = (20 +- sqrt(380))/2 = (20 +- 2*sqrt(95))/2 = 10 +- sqrt(95)

Ответ: x = 10 + sqrt(95), x = 10 - sqrt(95)