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cashatrofimov
@cashatrofimov
July 2022
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Помогите решить неравенство
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sangers1959
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(5x-13)*log₂ₓ₋₅(x²-6x+10)≥0
ОДЗ: 2x-5>0 x>5/2 2x-5≠1 x≠3 x²-6x+10>0 (x-3)²+1≡>0 ⇒ x∈(5/2;3)U(3;+∞)
2x-5>1 2x>6 x>3
5x-13≥0 5x>13 x>13/5
log₂ₓ₋₅(x²-6x+10)≥0 x²-6x+10≥(2x-5)° x²-6x+10≥1 x²-6x+9≥0 (x-3)²≡≥0 ⇒
x∈(3;+∞)
0<2x-5<1 5/2<x<3
5x-13≤0 x≤13/5
log₂ₓ₋₅(x²-6x+10)≤0 x²-6x+10≥(2x-5)° x²-6x+10≥1 x²-6x+9≥0 (x-3)²≡≥0 ⇒
x∈(5/2;13/5] ⇒
Ответ: x∈(5/2;13/5]U(3;+∞).
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Answers & Comments
Verified answer
(5x-13)*log₂ₓ₋₅(x²-6x+10)≥0ОДЗ: 2x-5>0 x>5/2 2x-5≠1 x≠3 x²-6x+10>0 (x-3)²+1≡>0 ⇒ x∈(5/2;3)U(3;+∞)
2x-5>1 2x>6 x>3
5x-13≥0 5x>13 x>13/5
log₂ₓ₋₅(x²-6x+10)≥0 x²-6x+10≥(2x-5)° x²-6x+10≥1 x²-6x+9≥0 (x-3)²≡≥0 ⇒
x∈(3;+∞)
0<2x-5<1 5/2<x<3
5x-13≤0 x≤13/5
log₂ₓ₋₅(x²-6x+10)≤0 x²-6x+10≥(2x-5)° x²-6x+10≥1 x²-6x+9≥0 (x-3)²≡≥0 ⇒
x∈(5/2;13/5] ⇒
Ответ: x∈(5/2;13/5]U(3;+∞).