(3 - 2√2)ˣ + (3 + 2√2)ˣ = 34
(3 - 2√2) (3 + 2√2) = 3² - (2√2)² = 9 - 8 = 1
(3 - 2√2) = 1 / (3 + 2√2)
(3 + 2√2)ˣ = t > 0
1/t + t = 34
t² - 34t + 1 = 0
D = 1156 - 4 = 1152 = 2⁷*3²
t1`2 = (34 +- 24√2)/2 = 17 +- 12√2 = 9 +- 2*3*2√2 + 8 = 3² +- 2*3*2√2
+ (2√2)² = (3 +- 2√2)²
t1 = (3 + 2√2)²
(3 + 2√2)ˣ = (3 + 2√2)²
x = 2
t1 = (3 - 2√2)²
(3 + 2√2)ˣ = 1 / (3 + 2√2)²
x = -2
ответ x = {-2, 2}
(3 - 2√2)ˣ + (3 + 2√2)ˣ = 34
(3 - 2√2) (3 + 2√2) = 3² - (2√2)² = 9 - 8 = 1
(3 - 2√2) = 1 / (3 + 2√2)
(3 + 2√2)ˣ = t > 0
1/t + t = 34
t² - 34t + 1 = 0
D = 1156 - 4 = 1152 = 2⁷*3²
t1`2 = (34 +- 24√2)/2 = 17 +- 12√2 = 9 +- 2*3*2√2 + 8 = 3² +- 2*3*2√2
+ (2√2)² = (3 +- 2√2)²
t1 = (3 + 2√2)²
(3 + 2√2)ˣ = (3 + 2√2)²
x = 2
t1 = (3 - 2√2)²
(3 + 2√2)ˣ = 1 / (3 + 2√2)²
x = -2
ответ x = {-2, 2}