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mLg
@mLg
August 2022
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3^x-3+1/3*3^x>10 Решите неравенство
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nKrynka
Решение
3^(x-3) + (1/3)*3^x > 10
(1/27)*(3^x)
+ (1/3)*3^x >
10 умножим на 27
3^x + 9*(3^x) > 270
10*(3^x) > 270
3^x > 27
3^x > 3
³
так как 3 > 1, то
x > 3
x
∈ (3; + ∞)
1 votes
Thanks 1
mLg
Спасибо большое, а откуда 27?
nKrynka
27 знаменателе первого слагаемого
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Answers & Comments
3^(x-3) + (1/3)*3^x > 10
(1/27)*(3^x) + (1/3)*3^x > 10 умножим на 27
3^x + 9*(3^x) > 270
10*(3^x) > 270
3^x > 27
3^x > 3³
так как 3 > 1, то
x > 3
x ∈ (3; + ∞)