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keizdub
@keizdub
July 2022
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2*3^-2x+2=3^-x+1 +1 решите ур-е
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ДенисЧ
2*3^-2x+2 = 3^-x+1 + 1
18*3^-2x - 3*3^-x - 1 = 0
3^-x = y
18y^2 - 3y - 1 = 0 OДЗ: y > 0
D = b^2 - 4ac = 9 + 4*18 = 81, D > 0, √D = 9
y1,2 = (-b ± √D)/2a = (3
± 9)/36
y1 = -1/6
∉ ОДЗ
y2 = 1/3
3^-x = 1/3
x = 1
Ответ: х = 1
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Answers & Comments
18*3^-2x - 3*3^-x - 1 = 0
3^-x = y
18y^2 - 3y - 1 = 0 OДЗ: y > 0
D = b^2 - 4ac = 9 + 4*18 = 81, D > 0, √D = 9
y1,2 = (-b ± √D)/2a = (3 ± 9)/36
y1 = -1/6 ∉ ОДЗ
y2 = 1/3
3^-x = 1/3
x = 1
Ответ: х = 1