Question

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rozwiąż nierówność
4x² - 1 ≥ 0 2 b) 4x² - 5x < x² + 4x​

Answer 1

Verified answer

a)

[tex]4x^{2}-1 \geq 0\\\\M. \ zerowe\\\\(2x+1)(2x-1) =0\\\\2x = -1 \ \vee \ 2x = 1\\\\x = -\frac{1}{2} \ \vee \ x = \frac{1}{2}\\\\a > 0, \ to \ ramiona \ paraboli \ skierowane \ do \ gory\\\\x\in (-\infty;-\frac{1}{2}\rangle \ \cup \ \langle\frac{1}{2};+\infty)[/tex]

b)

[tex]4x^{2}-5x < x^{2}+4x\\\\4x^{2}-x^{2}-5x-4x < 0\\\\3x^{2}-9x < 0\\\\3(x^{2}-3x) < 0 \ \ \ /:3\\\\x^{2}-3x < 0\\\\M. \ zerowe:\\\\x^{2}-3x = 0\\\\x(x-3) = 0\\\\x = 0 \ \vee \ x = 3\\\\a > 0, \ ramiona \ paraboli \ skierowane \ do \ gory\\\\x \in (0;3)[/tex]