Question

Rezolvati pas cu pas, pe foaie scris de mana

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{1}{ \sqrt{7} - \sqrt{8} } + \frac{1}{ \sqrt{7} + \sqrt{8} } + 2 \sqrt{7}$

$= \frac{ {}^{ \sqrt{7} + 2 \sqrt{2}) } 1}{ \sqrt{7} - 2 \sqrt{2} } + \frac{ {}^{ \sqrt{7} - 2 \sqrt{2} )} 1}{ \sqrt{7} + 2 \sqrt{2} } + 2 \sqrt{7}$

$= \frac{ \sqrt{7} + 2 \sqrt{2} }{( \sqrt{7} - 2 \sqrt{2})(7 + 2 \sqrt{2}) } + \frac{ \sqrt{7} - 2 \sqrt{2} }{( \sqrt{7} - 2 \sqrt{2})(7 + 2 \sqrt{2} ) } + 2 \sqrt{7}$

$= \frac{ \sqrt{7} + 2 \sqrt{2} }{( \sqrt{7}) {}^{2} - (2 \sqrt{2}) {}^{2} } + \frac{ \sqrt{7} - 2 \sqrt{2} }{( \sqrt{7}) {}^{2} - (2 \sqrt{2}) {}^{2} } + 2 \sqrt{7}$

$= \frac{ \sqrt{7} + 2 \sqrt{2} }{7 - 8} + \frac{ \sqrt{7} - 2 \sqrt{2} }{7 - 8} + 2 \sqrt{7}$

$= \frac{ \sqrt{7} + 2 \sqrt{2} }{ - 1} + \frac{ \sqrt{7} - 2 \sqrt{2} }{ - 1} + 2 \sqrt{7}$

$= - ( \sqrt{7} + 2 \sqrt{2} ) - ( \sqrt{7} - 2 \sqrt{2} ) + 2 \sqrt{7}$

$= - \sqrt{7} - 2 \sqrt{2} - \sqrt{7} + 2 \sqrt{2} + 2 \sqrt{7}$

$= - 2 \sqrt {7} + 2 \sqrt {7} = 0$