Question

розв'язати рівняння
(3 - 2√2)^х + (3 + 2√2)^х = 6​

Answer 1

Ответ:

Объяснение:

(3 - 2√2)^х + (3 + 2√2)^х = 6​

(3 - 2√2)^х * (3 + 2√2)^х = ((3)^2 - (2√2)^2)^х =(9 - 4*2)^х =1^х = 1

(3 - 2√2)^х = t

(3 + 2√2)^х = 1/t

t + 1/t =6

t^2 - 6t +1 = 0

D = 36 -4 = 32

t 1 = (6 -4√2)/2 = (3 - 2√2) = (3 - 2√2)^х => x1 = 1

t 2 = (6 +4√2)/2 = (3 + 2√2) = (3 - 2√2)^х => x2 = - 1

ответ, х є {-1; 1}