Question

решите уравнение
$(2-x sqrt{6} ) sqrt{2} =2(x- sqrt{6})$

Answer 1

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