2^(x^2-1)-3^(x^2)=3^(x^2-1)-2^(x^2+2) - вопрос №736225122132321222 от Elaria1 27.09.2022 12:13

Question

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

Elaria1 · Answer

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