Решите квадратные неравенства.. Created by KeitOstin. matematika-ru

Решите квадратные неравенства...

KeitOstin @KeitOstin

August 2021 1 8 Report

Решите квадратные неравенства.

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IrkaShevko

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$\frac{x-1}{x-3} \ \textless \ 3\\
 \frac{x-1}{x-3} - \frac{3x-9}{x-3} \ \textless \ 0\\
 \frac{8-2x}{x-3} \ \textless \ 0\\
....-...(3)...........+.........(4).....-......\\
x\in(- \infty; 3)U(4;+\infty)$

$\frac{x-2}{x+4} \ \textgreater \ \frac{x+4}{x-2} \\
 \frac{(x-2)^2-(x+4)^2}{(x-2)(x+4)} \ \textgreater \ 0\\
 \frac{x^2-4x+4-x^2-8x-16}{(x-2)(x+4)} \ \textgreater \ 0\\
 \frac{-12x-12}{(x-2)(x+4)} \ \textgreater \ 0\\
....+......(-4)....-......(-1).....+.....(2).....-......\\
x\in (-\infty;-4)U(-1;2)$

4) _-___(-3)___+_____(2)____-____(4)_____+___
x∈(-∞; -3) U (2; 4)

5) __+_(-3)___-___(1)___+___(2)__-____(4)__+__
x∈(-∞; -3) U (1; 2) U (4; +∞)

2 votes Thanks 1

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