Question

Efectuati:

a) (radical din 3/2 -3 radical din 2+ 1/radical din 3+ 1/radical din 2) :(1/2 radical din 3 -1/radical din 2)=

Answer 1

( $\frac{ \sqrt{3} }{2}$ - $\frac{3 \sqrt{2} + 1}{ \sqrt{3} }$ + $\frac{1}{ \sqrt{2} }$ ) : ( $\frac{1}{ 2\sqrt{3} }$ - $\frac{1}{ \sqrt{2} }$ ) = 
 [ 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.]
 = $-\frac{7 + 2 \sqrt{6} - 6 \sqrt{2} - 12 \sqrt{3} }{5}$.