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korzhmargarita
@korzhmargarita
July 2022
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Помогите пожалуйста дорешать))) Сейчас!
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natali3221
10^x-5·2^x-8·5^x+40≤0
2^x·5^x-5·2^x-8·5^x+8·5≤0
(2^x·5^x-5·2^x)-(8·5^x-8·5)≤0
2^x(5^x-5)-8(5^x-5)≤0
(2^x-8)(5^x-5)≤0
2^x-8≤0 или 2^x-8≥0
5^x-5≥0 5^x-5≤0
2^x≤8 2^x≥8
5^x≥5 5^x≤5
2^x≤2³ 2^x≥2³
5^x≥5^1 5^x≤5^1
x≤3 x≥3
x≥1 x≤1
x∈[1 ; 3 ] x∈Ф
Ответ: х∈[1 ; 3 ]
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Answers & Comments
2^x·5^x-5·2^x-8·5^x+8·5≤0
(2^x·5^x-5·2^x)-(8·5^x-8·5)≤0
2^x(5^x-5)-8(5^x-5)≤0
(2^x-8)(5^x-5)≤0
2^x-8≤0 или 2^x-8≥0
5^x-5≥0 5^x-5≤0
2^x≤8 2^x≥8
5^x≥5 5^x≤5
2^x≤2³ 2^x≥2³
5^x≥5^1 5^x≤5^1
x≤3 x≥3
x≥1 x≤1
x∈[1 ; 3 ] x∈Ф
Ответ: х∈[1 ; 3 ]