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}
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Verified answer
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}