Răspuns:
[tex]s = \frac{ - 5 \sqrt{6 } + \sqrt{30} }{ \sqrt{6} \times ( \sqrt{5} - 5)} [/tex]
Explicație pas cu pas:
=>
[tex]s = \frac{(1 - \sqrt{2} ) \sqrt{2} }{2} + \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{6} } + \frac{ \sqrt{3} - 2 }{2 \sqrt{3} } + \frac{2 - \sqrt{5} }{2 \sqrt{5} } ) \times \frac{5}{ \sqrt{5} - 5} [/tex]
[tex]s = ( \frac{ \sqrt{2} - 2 }{2} + \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{6} } + \frac{( \sqrt{3} - 2) \sqrt{3} }{ {10} } ) \times \frac{5}{ \sqrt{5} - 5 } [/tex]
[tex]s = ( \frac{ \sqrt{2} - 2 }{2} + \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{6} } + \frac{3 - 2 \sqrt{3} }{6} + \frac{2 \sqrt{5} - 5 }{10} ) \times \frac{5}{ \sqrt{5} - 5 } [/tex]
[tex]s = ( \frac{15( \sqrt{2} - 2) + 5(3 - 2 \sqrt{3} ) + 3(2 \sqrt{5} - 5) }{30} + \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{6} } ) \times \frac{5}{ \sqrt{5 } - 5 } [/tex]
[tex]s = \frac{ \sqrt{6} \times (15 \sqrt{2} - 30 - 10 \sqrt{3} + 6 \sqrt{5} ) + 30( \sqrt{2} - \sqrt{3} ) }{30 \sqrt{6} } \times \frac{5}{ \sqrt{5} - 5 } [/tex]
[tex]s = \frac{ - 30 \sqrt{6 } - 30 \sqrt{2} + 6 \sqrt{30} + 30 \sqrt{2} }{6 \sqrt{6} } \times \frac{1}{ \sqrt{5} - 5} [/tex]
[tex]s = \frac{ - 5 \sqrt{6} + \sqrt{30} }{ \sqrt{6} } \times \frac{1}{ \sqrt{5} - 5} [/tex]
[tex]s = \frac{ - 5 \sqrt{6} + \sqrt{30} }{ \sqrt{6} \times ( \sqrt{5} - 5 )} [/tex]
