Răspuns:
Explicație pas cu pas:
[tex] \frac{1}{ \sqrt{7} - \sqrt{8} } + \frac{1}{ \sqrt{7} + \sqrt{8} } + 2 \sqrt{7} \\ [/tex]
[tex] = \frac{ {}^{ \sqrt{7} + 2 \sqrt{2}) } 1}{ \sqrt{7} - 2 \sqrt{2} } + \frac{ {}^{ \sqrt{7} - 2 \sqrt{2} )} 1}{ \sqrt{7} + 2 \sqrt{2} } + 2 \sqrt{7} \\ [/tex]
[tex] = \frac{ \sqrt{7} + 2 \sqrt{2} }{( \sqrt{7} - 2 \sqrt{2})(7 + 2 \sqrt{2}) } + \frac{ \sqrt{7} - 2 \sqrt{2} }{( \sqrt{7} - 2 \sqrt{2})(7 + 2 \sqrt{2} ) } + 2 \sqrt{7} \\ [/tex]
[tex] = \frac{ \sqrt{7} + 2 \sqrt{2} }{( \sqrt{7}) {}^{2} - (2 \sqrt{2}) {}^{2} } + \frac{ \sqrt{7} - 2 \sqrt{2} }{( \sqrt{7}) {}^{2} - (2 \sqrt{2}) {}^{2} } + 2 \sqrt{7} \\ [/tex]
[tex] = \frac{ \sqrt{7} + 2 \sqrt{2} }{7 - 8} + \frac{ \sqrt{7} - 2 \sqrt{2} }{7 - 8} + 2 \sqrt{7} \\ [/tex]
[tex] = \frac{ \sqrt{7} + 2 \sqrt{2} }{ - 1} + \frac{ \sqrt{7} - 2 \sqrt{2} }{ - 1} + 2 \sqrt{7} \\ [/tex]
[tex] = - ( \sqrt{7} + 2 \sqrt{2} ) - ( \sqrt{7} - 2 \sqrt{2} ) + 2 \sqrt{7} \\ [/tex]
[tex] = - \sqrt{7} - 2 \sqrt{2} - \sqrt{7} + 2 \sqrt{2} + 2 \sqrt{7} \\ [/tex]
[tex] = - 2 \sqrt {7} + 2 \sqrt {7} = 0 [/tex]
