Explicație pas cu pas:
[tex]a = \left( \frac{ | \sqrt{18} - 3| }{9} + \frac{ |2 \sqrt{8} - 6| }{24} + \frac{ | \sqrt{50} - 10| }{30} \right) \div \left( \frac{3 \sqrt{5} }{\sqrt{90} } \right) \\ =[/tex]
[tex] = \left( \frac{ 3\sqrt{2} - 3 }{9} + \frac{6 - 4 \sqrt{2}}{24} + \frac{10 - 5 \sqrt{2} }{30} \right) \div \left( \frac{3 \sqrt{5} }{3\sqrt{10} } \right) \\ [/tex]
[tex]= \left( \frac{ 3(\sqrt{2} - 1)}{9} + \frac{2(3 - 2 \sqrt{2})}{24} + \frac{5(2 - \sqrt{2}) }{30} \right) \div \left( \frac{1}{\sqrt{2} } \right) \\ [/tex]
[tex]= \left( \frac{ 3(\sqrt{2} - 1)}{9} + \frac{2(3 - 2 \sqrt{2})}{24} + \frac{5(2 - \sqrt{2}) }{30} \right) \times \sqrt{2} \\ [/tex]
[tex]= \left( \frac{ \sqrt{2} - 1}{3} + \frac{3 - 2 \sqrt{2}}{12} + \frac{2 - \sqrt{2}}{6} \right) \times \sqrt{2} \\ [/tex]
[tex]= \left(\frac{4( \sqrt{2} - 1)}{12} + \frac{3 - 2 \sqrt{2}}{12} + \frac{2(2 - \sqrt{2})}{12} \right) \times \sqrt{2} \\ [/tex]
[tex]= \frac{ (4\sqrt{2} - 4 + 3 - 2 \sqrt{2} + 4 - 2 \sqrt{2} )}{12} \times \sqrt{2} \\ [/tex]
[tex]= \frac{3}{12} \times \sqrt{2} = \frac{ \sqrt{2} }{4} \\ [/tex]
