Решите уравнение: (x^2 + 49/x^2) - 8(x - 7/x) = 2

Question

Решите уравнение:

(x^2 + 49/x^2) - 8(x - 7/x) = 2

Answer 1

(x^2 + 49/x^2) - 8(x - 7/x) = 2

x^2+49/x^2(-8x+56/x)*(x)=2*x^2

x^2+49-8x^2+56x-2x^2=0

-9x^2+56x+49=0 
D = b2 - 4ac
D = 3136 + 1764 = 4900 = 70^2

x1,2 = -b ± √D/2a
x1 = -56 + 70/-18 = - 14/18 = - 7/9
x2 = -56 - 70/-18= 126/18= 7
Ответ: x1 = - 7/9; x2 = 7