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n6476761
@n6476761
July 2022
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решите неравенство (x^5-x^2)/x^2>=(x^3-1)/4x^2
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Юленька194
Verified answer
Если есть вопросы пишите
29 votes
Thanks 6
Нафаня88
X⁵-x²
\
x²≥x³-1
\
4x² ОДЗ: 4х²≠0 x≠2 x≠-2
x²(x³-1)
\
x² - (x³-1)
\
4x²≥0
4x²*(x³-1) -(x³-1
)\
4x²≥0
(4x³-1)(x³-1)
\
4x²≥0
система:
4x²-1≥0; x²≥0,25 x≥+-0,5 x∈ (-∞;-0,5]∪[0,5;+∞)
x³-1≥0; x³≥1 x≥1 x∈ [1;+∞)
ответ: (-∞;-2]∪[2;+∞)
13 votes
Thanks 3
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Answers & Comments
Verified answer
Если есть вопросы пишитеx²(x³-1)\x² - (x³-1)\4x²≥0
4x²*(x³-1) -(x³-1)\4x²≥0
(4x³-1)(x³-1)\4x²≥0
система:
4x²-1≥0; x²≥0,25 x≥+-0,5 x∈ (-∞;-0,5]∪[0,5;+∞)
x³-1≥0; x³≥1 x≥1 x∈ [1;+∞)
ответ: (-∞;-2]∪[2;+∞)