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Rauau1999
@Rauau1999
July 2022
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pomoshnik09
3^(2x)-4*3^x*2^x+3^x*2^x+3*2^(2x)-8*6^x=0
3^2x-4*6^x+6^x+3*2^(2x)-8*6^x=0
3^(2x)-4*6^x+3*2^(2x)=0 разделим на 2^(2x)
3/2)^(2x)-4*(3/2)^x+3=0 пусть 3/2)^x=n
n²-4n+3=0 D=4²-4*1*3=16-12=4 n1=(4+√4)/2=3 n2=4-2)/2=1
(3/2)^x=3 x=log3/2 3
3/2)^x=1 (3/2)^x=(3/2)^0 x=0
ответ log3/2 3. 0
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Answers & Comments
3^2x-4*6^x+6^x+3*2^(2x)-8*6^x=0
3^(2x)-4*6^x+3*2^(2x)=0 разделим на 2^(2x)
3/2)^(2x)-4*(3/2)^x+3=0 пусть 3/2)^x=n
n²-4n+3=0 D=4²-4*1*3=16-12=4 n1=(4+√4)/2=3 n2=4-2)/2=1
(3/2)^x=3 x=log3/2 3
3/2)^x=1 (3/2)^x=(3/2)^0 x=0
ответ log3/2 3. 0