Question

1/2^(2+x) -1/2^(2-x) =-3/8 Помогите решить уравнение, пожалуйста.

Answer 1

1/2^(2+x) -1/2^(2-x) =-3/8

1/2^2*1/2^(x) - 1/2^2*1/2^(-x) =-3/8

1/4*1/2^(x) -1/4*1/2^(-x) =-3/8

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

1/2^x = y > 0

y - 1/y + 3/2 = 0

(2y^2 + 3y - 2)/2y = 0

 2y^2 + 3y - 2 = 0

D = 9 + 4*2*2 = 25

y12 = (-3 +- 5)/4 = -2   1/2

y1 = -2 < 0 нет

y2 = 1/2

1/2^x = 1/2

x = 1