Răspunsuri

2014-11-01T18:41:46+02:00
Ridici numarul la patrat si dupa acea efectuezi calculul!

Cel mai inteligent răspuns!
2014-11-01T19:39:16+02:00
(  \frac{ \sqrt{3} }{2} -  \frac{3 \sqrt{2} + 1}{ \sqrt{3} } +  \frac{1}{ \sqrt{2} } ) : (  \frac{1}{ 2\sqrt{3} } -   \frac{1}{ \sqrt{2} } ) = 
 [ Amplificam prima fractie cu  \sqrt{6} ; a 2-a cu  2\sqrt{2} ; a3-a fractie cu  2\sqrt{3} ; a4-a cu  \sqrt{2} ; a 5- a cu  2\sqrt{3} ]
=  \frac{ \sqrt{18} -  6\sqrt{4} -  2\sqrt{2} +  2\sqrt{3}  }{ 2\sqrt{6} } : (  \frac{ \sqrt{2}  -  2\sqrt{3} }{ 2\sqrt{6} } ) =
=  \frac{3 \sqrt{2} - 12 -  2\sqrt{2} +  2\sqrt{3}   } {2 \sqrt{6} } ·  \frac{2 \sqrt{6} }{ \sqrt{2} - 2 \sqrt{3} } =
 [ Aici se simplifica cu   2\sqrt{6} ]
 =  \frac{ \sqrt{2}- 12  + 2 \sqrt{3} }{ \sqrt{2} - 2 \sqrt{3} } =
 [ Rationalizam cu  \sqrt{2} + 2 \sqrt{3} ]
 =  \frac{ (\sqrt{2}  + 2 \sqrt{3} - 12)(  \sqrt{2} + 2 \sqrt{3}  )} { ( \sqrt{2} )^{2} -  (2 \sqrt{3} )^{2}  } =
 =  \frac{2 + 2 \sqrt{6} + 2 \sqrt{6} + 12 - 12 \sqrt{2} - 24 \sqrt{3}    }{2 - 12} =
 =  \frac{14 + 4 \sqrt{6} - 12 \sqrt{2} - 24 \sqrt{3}   }{- 10} =
 = - \frac{2 ( 7 + 2 \sqrt{6} - 6 \sqrt{2} - 12 \sqrt{3}   )}{10} =
 [ Simplificam 10  cu  2.]
 =  -\frac{7 + 2 \sqrt{6} - 6 \sqrt{2} - 12 \sqrt{3}   }{5} .
unde simplific cu 2 radical 6???
Aici : \frac{3 \sqrt{2} - 12 - 2\sqrt{2} + 2\sqrt{3} } {2 \sqrt{6} } · \frac{2 \sqrt{6} }{ \sqrt{2} - 2 \sqrt{3} } . 2 radical din 6 din stanga jos cu 2 radical din 6 din dreapta sus.