Решите неравенство [tex] log_{x} \sqrt{21-4x} \ \textgreater \ 1[/tex]. Created by emilynight1. matematika-ru

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emilynight1 @emilynight1

July 2022 1 7 Report

Решите неравенство [tex] log_{x} \sqrt{21-4x} \ \textgreater \ 1[/tex]

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hote

Verified answer

$Log_x( \sqrt{21-4x)}\ \textgreater \ 1$

ОДЗ:
$21-4x\ \textgreater \ 0$
$4x\ \textless \ 21$
$x\ \textless \ 5.25$

$x\ \textgreater \ 0; x \neq 1$

$ODZ (0;1) (1;5.25)$

1 случай

$0\ \textless \ x\ \textless \ 1$

$\sqrt{21-4x}\ \textless \ x^1$

$21-4x\ \textless \ x^2$

$x^2+4x-21\ \textgreater \ 0

D=16+84=100

x=-7; x=3

$

Решений нет т.к. 0<x<1 и (-∞;-7)(3;+∞) не пересекаются

2случай

1<x<5.25

$\sqrt{21-4x}\ \textgreater \ x^1$

$x^2+4x-21\ \textless \ 0$

1<x<5.25
-7<x<3

Ответ (1;3)

1 votes Thanks 2

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emilynight1 August 2022 | 0 Ответы

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