[tex] \sqrt{x-6}* \sqrt{x-12}\ \textless \ x-1 [/tex]. Created by sandy00. algebra-ru

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sandy00 @sandy00

September 2021 1 13 Report

[tex] \sqrt{x-6}* \sqrt{x-12}\ \textless \ x-1 [/tex]

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eugeke

Verified answer

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

$\left\{\begin{matrix}
x-1 &\ \textgreater \ &0 \\ 
(x-6)(x-12) &\ \textless \ &(x-1)^2 \\ 
x-6 &\geqslant &0 \\ 
x-12 &\geqslant &0 
\end{matrix}\right.$

$x-1\ \textgreater \ 0\\
x\ \textgreater \ 1\\
x\in(1;+\infty)$

$(x-6)(x-12)\ \textless \ (x-1)^2\\
(x-6)(x-12)-(x-1)^2\ \textless \ 0\\
x^2-18x+72-x^2+2x-1\ \textless \ 0\\
-16x\ \textless \ -71\\\\
x\ \textgreater \ \frac{71}{16}\\\\
x\in(\frac{71}{16};+\infty)$

$x-6\geqslant 0\\
x\geqslant 6\\
x\in[6;+\infty)\\\\\\
x-12\geqslant 0\\
x\geqslant 12\\
x\in(12;+\infty)$

Ответ: $x\in[12;+\infty)$

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