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altulsk
@altulsk
August 2022
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(√2-1)^x+(√2+1)^x -2=0
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ЕкарныйБабай
Verified answer
(√2-1)^x+(√2+1)^x -2=0
заметим
√2-1=1/(√2+1)
t=(√2-1)^x >0
t+1/t-2=0
t²-2t+1=0
(t-1)²=0
t=1
(√2-1)^x=1
(√2-1)^x=(√2-1)^0
x=0
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Answers & Comments
Verified answer
(√2-1)^x+(√2+1)^x -2=0заметим √2-1=1/(√2+1)
t=(√2-1)^x >0
t+1/t-2=0
t²-2t+1=0
(t-1)²=0
t=1
(√2-1)^x=1
(√2-1)^x=(√2-1)^0
x=0