решите уравнение [tex](2-x \sqrt{6} ) \sqrt{2} =2(x- \sqrt{6}) [/tex]. Created by taniachaika61. algebra-ru

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July 2022 1 7 Report

решите уравнение
[tex](2-x \sqrt{6} ) \sqrt{2} =2(x- \sqrt{6}) [/tex]

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Firuza25 $(2-x \sqrt{6}) \sqrt{2} = 2(x- \sqrt{6}$
$2 \sqrt{2} -x \sqrt{12} =2x-2 \sqrt{6}$
$2 \sqrt{2} -2x \sqrt{3} =2x-2 \sqrt{6}$
$2x \sqrt{3}+2x=2 \sqrt{6}+2 \sqrt{2}$
$2x( \sqrt{3}+1)=2( \sqrt{6}+ \sqrt{2})$
$x( \sqrt{3}+1)=( \sqrt{6} + \sqrt{2} )$
$x= \frac{ \sqrt{6}+ \sqrt{2}}{ \sqrt{3}+1} = \frac{( \sqrt{6}+ \sqrt{2})( \sqrt{3}-1)}{( \sqrt{3}+1)( \sqrt{3}-1)} = \frac{ \sqrt{18}- \sqrt{6}+ \sqrt{6}- \sqrt{2}}{3-1}= \frac{ \sqrt{18}- \sqrt{2}}{2}= \frac{3 \sqrt{2}- \sqrt{2}}{2}= \\ = \frac{2 \sqrt{2}}{2}= \sqrt{2}$

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