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YesKinder
@YesKinder
July 2022
2
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9*(6/5)^x-5*(5/6)^(x-1)-3=0
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ВладимирБ
Verified answer
Решение смотри в приложении
1 votes
Thanks 1
oganesbagoyan
Verified answer
9*(6/5)^x-5*(5/6)^(x-1)-3=0 ;
9*(6/5)^x-5*(5/6)^x*(5/6)^(-1) -3=0 ; * * * (5/6) ^(-1) =1 /(5/6)^1 =6/5 * * *
9*(6/5)^x-6*(5/6)^x -3=0 ;
3*
(6/5)^x-2*(5/6)^x -1=0 ;
замена переменной: t =(5/6)^x >0 ⇒ (6/5)^x =1/t .
3/t -2t -1 =0 ;
2t² +t -3 =0 ;
t₁= (-1-5)/(2*2) = -3/2 (не корень исходного уравнения)
t₂= (-1+5)/(2*2) = 1 ⇒ (5/6)^x =1⇔ (5/6)^x =(5/6)⁰
⇒ x =0.
ответ : 0.
0 votes
Thanks 0
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Answers & Comments
Verified answer
Решение смотри в приложенииVerified answer
9*(6/5)^x-5*(5/6)^(x-1)-3=0 ;9*(6/5)^x-5*(5/6)^x*(5/6)^(-1) -3=0 ; * * * (5/6) ^(-1) =1 /(5/6)^1 =6/5 * * *
9*(6/5)^x-6*(5/6)^x -3=0 ;
3*(6/5)^x-2*(5/6)^x -1=0 ;
замена переменной: t =(5/6)^x >0 ⇒ (6/5)^x =1/t .
3/t -2t -1 =0 ;
2t² +t -3 =0 ;
t₁= (-1-5)/(2*2) = -3/2 (не корень исходного уравнения)
t₂= (-1+5)/(2*2) = 1 ⇒ (5/6)^x =1⇔ (5/6)^x =(5/6)⁰ ⇒ x =0.
ответ : 0.