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

Question

Алгебра

Еленя

29 ноября, 11:29

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

+2

Ответы (1)

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Кириак · Answer 1

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

2^ (x^2-1) - 3^ (x^2) - 3^ (x^2-1) + 2^ (x^2+2) = 0 / : 3^x^2

(2/3) ^ (x^2) * 1/2 - 1 - 1*1/3 + (2/3) ^ (x^2) * 4 = 0

(2/3) ^ (x^2) * 1/2 - 4/3 + (2/3) ^ (x^2) * 4 = 0

(2/3) ^ (x^2) * 1/2 + (2/3) ^ (x^2) * 4 = 4/3

(2/3) ^ (x^2) * (1/2 + 4) = 4/3

(2/3) ^ (x^2) * (9/2) = 4/3

(2/3) ^ (x^2) = 8/27

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

x^2 = 3

x = ± √3

Ответ

- √3; √3