Решите неравенство: (9x^2-4)(16-x^2)(2x^2+3)>0. Created by nadiabakrova03. algebra-ru

Решите неравенство: (9x^2-4)(16-x^2)(2x^2+3)>0...

nadiabakrova03 @nadiabakrova03

April 2021 1 10 Report

Решите неравенство:
(9x^2-4)(16-x^2)(2x^2+3)>0

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Dимасuk

Verified answer

По формуле разности квадратов:
(3x - 2)(3x + 2)(4 - x)(4 + x)(2x² + 3) > 0
2x² + 3 > 0 при любых x, т.к. сумма квадрата числа с положительным числом будет принимать положительные значения.
Решаем неравенство:
(3x - 2)(3x + 2)(4 - x)(4 + x) > 0
(3x - 2)(3x + 2)(x - 4)(x + 4) < 0
Нули: x = -4; -2/3; 2/3; 4.
||||||||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||||||||||
-----------(-4)----------------------(-2/3)--------(2/3)-----------------------(4)--------->x
+ - + - +

Ответ: x ∈ (-4; -2/3) U (2/3; 4).

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