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marsvnas0111
@marsvnas0111
August 2022
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Решить уравнение.
4^x+2*6^x-3*9^x=0
прошу,помогите
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nKrynka
4^x+2*6^x-3*9^x=0
(2^2X) + 2*2^x*3^x - 3*(3^2x) = 0 /( 3^2x)
(2/3)^2 + 2*(2/3)^x - 3 = 0
(2/3)^x = z, z> 0
z^2 + 2z - 3 = 0
z1 = - 3
z2 = 1
(2/3)^x = -3, не удовлетворяет условию: z > 0
(2/3)^x = 1
(2/3)^x = (2/3)^0
x = 0
Ответ: х = 0
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Answers & Comments
(2^2X) + 2*2^x*3^x - 3*(3^2x) = 0 /( 3^2x)
(2/3)^2 + 2*(2/3)^x - 3 = 0
(2/3)^x = z, z> 0
z^2 + 2z - 3 = 0
z1 = - 3
z2 = 1
(2/3)^x = -3, не удовлетворяет условию: z > 0
(2/3)^x = 1
(2/3)^x = (2/3)^0
x = 0
Ответ: х = 0