Question

$2^{x+2}-2^{2-x}=15$

Answer 1

4*2^(x) - 4*2^(-x) = 15
Замена: 2^(x) = t > 0
4t - 4/t = 15
(4t^2 - 4)/t = 15
15t = 4t^2 - 4
4t^2 - 15t - 4 = 0, D = 289
t1 = (15 - 17)/8 = -2/8 = -1/4 < 0 - посторонний корень
t2 = (15 + 17)/8 = 4 > 0
2^(x) = 4 = 2^2
x = 2