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ulyalyas
@ulyalyas
August 2022
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(√(6+√35))^x+(√(6-√35))^x=12 ПОШАГОВО, пожалуйста, внутри картинка уравнения
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sedinalana
6-√35=1/(6+√35)
--------------------------
(6+√35)^(x/2)+1/(6+√35)^9x/2)-12=0
(6+√35)^(x/2)=a
a+1/a-12=0
a²-12a+1=0
D=144-4=140
√D=2√35
a1=(12-2√35)/2=6-√35⇒(6+√35)^(x/2)=6-√35⇒(6+√35)^(x/2)=(6+√35)^-1⇒
⇒x/2=-1⇒x=-2
a2=6+√35⇒(6+√35)^(x/2)=6+√35⇒x/2=1⇒x=2
Ответ x=-2,x=2
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Answers & Comments
--------------------------
(6+√35)^(x/2)+1/(6+√35)^9x/2)-12=0
(6+√35)^(x/2)=a
a+1/a-12=0
a²-12a+1=0
D=144-4=140
√D=2√35
a1=(12-2√35)/2=6-√35⇒(6+√35)^(x/2)=6-√35⇒(6+√35)^(x/2)=(6+√35)^-1⇒
⇒x/2=-1⇒x=-2
a2=6+√35⇒(6+√35)^(x/2)=6+√35⇒x/2=1⇒x=2
Ответ x=-2,x=2