Помогите пожалуйста решить неравенство: [tex]\sqrt{x-6} *\sqrt{x-12} \ \textless \ x-1[/tex]. Created by iriskaesipova. algebra-ru

Неравенство равносильно системеОтвет:

tex]...

iriskaesipova @iriskaesipova

August 2021 1 8 Report

Помогите пожалуйста решить неравенство:
[tex]\sqrt{x-6} *\sqrt{x-12} \ \textless \ x-1[/tex]

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NeZeRAvix

Verified answer

$\sqrt{x-6}\cdot \sqrt{x-12}\ \textless \ x-1$

Неравенство равносильно системе
$\left \{\begin{array}{I} x-6 \geq0 \\ x-12 \geq 0 \\ x-1 \geq 0 \\ \sqrt{x-6}\cdot \sqrt{x-12}\ \textless \ x-1 \end{array} \Leftrightarrow \left \{\begin{array}{I} x \geq 6 \\ x \geq 12 \\ x \geq 1 \\ x^2-18x+72 \textless \ x^2-2x+1 \end{array} \Leftrightarrow$
$\Leftrightarrow \left \{\begin{array}{I} x \geq 12 \\ 16x\ \textgreater \ 71\end{array} \Leftrightarrow \left \{\begin{array}{I} x \geq 12 \\ x\ \textgreater \ \dfrac{71}{16} \end{array} \Leftrightarrow x \geq 12$

Ответ: $x \in [12;\ + \infty)$

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iriskaesipova August 2022 | 0 Ответы

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iriskaesipova August 2022 | 0 Ответы

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iriskaesipova August 2022 | 0 Ответы

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Verified answer

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