Explicație pas cu pas:
[tex]a) \frac{2 \sqrt{27} }{ \sqrt{24} - \sqrt{3}( \sqrt{8} - 3) } = \frac{2 \times \sqrt{9 \times 3} }{ \sqrt{4 \times 6} - \sqrt{3}( \sqrt{4 \times 2} - 3) } = \\ = \frac{2 \times 3 \sqrt{3} }{2 \sqrt{6} - \sqrt{3} (2 \sqrt{2} - 3) } = \\ = \frac{6 \sqrt{3} }{2 \sqrt{6} - \sqrt{3} \times 2 \sqrt{2} - \sqrt{3} \times ( - 3) } \\ = \frac{6 \sqrt{3} }{2 \sqrt{6} - 2 \sqrt{6} + 3 \sqrt{3} } = \frac{6 \sqrt{3} }{3 \sqrt{3} } = \frac{6}{3} = 2 \: adevarat[/tex]
[tex]b)x = 6 \sqrt{3} ( \frac{1}{ \sqrt{3} } + \frac{1}{ \sqrt{6} } ) + \sqrt{24} ( \frac{1}{ \sqrt{6} } - \frac{ \sqrt{3} }{2} ) - \frac{2 \sqrt{27} }{ \sqrt{24 } - \sqrt{3} ( \sqrt{8} - 3)} \\ x = 6 \sqrt{3} ( \frac{ \sqrt{3} }{3} + \frac{ \sqrt{6} }{6} ) + 2 \sqrt{6} ( \frac{ \sqrt{6} }{6} - \frac{ \sqrt{3} }{2} ) - 2 \\ x = 6 \sqrt{3} \times (\frac{2 \sqrt{3} + \sqrt{6} } {6} ) + 2 \sqrt{6} \times ( \frac{ \sqrt{6} - 3 \sqrt{3} }{6} ) - 2 \\ x = 6 \sqrt{3} \times \frac{2 \sqrt{3} }{6} + 6 \sqrt{3} \times \frac{ \sqrt{6} }{6} + 2 \sqrt{6} \times \frac{ \sqrt{6} }{6} + 2 \sqrt{6} \times ( - \frac{3 \sqrt{3} }{6} ) - 2 \\ x = \frac{36}{6} + \frac{6 \sqrt{18} }{6} + \frac{12}{6} - \frac{6 \sqrt{18} }{6} - 2 \\ x = 6 + \sqrt{18} + 2 - \sqrt{18} - 2 \\ x = 6[/tex]
