Question

can any one do this ? pls

Answer 1

$7. \\ \frac{1}{ \sqrt{11 - 2 \sqrt{30} } } - \frac{3}{7 + 2 \sqrt{10} } - \frac{4}{ \sqrt{8 - 4 \sqrt{3} } } \\ = \frac{1} { \sqrt{({ \sqrt{5}) }^{2} + {( \sqrt{6}) }^{2} - 2 \times \sqrt{5} \times \sqrt{6} }} - \frac{1}{ \sqrt{ ({ \sqrt{5}) }^{2} + ({ \sqrt{2}) }^{2} + 2 \times \sqrt{5} \times \sqrt{2} } } - \frac{1}{ \sqrt{ ({ \sqrt{2}) }^{2} + ({ \sqrt{6} })^{2} - 2 \times \sqrt{2} \times \sqrt{6} } } \\ = \frac{1}{ \sqrt{ \ ({ \sqrt{5} - \sqrt{6} )}^{2}} } - \frac{1}{ \sqrt{( { \sqrt{5} + \sqrt{2} })^{2} }} - \frac{1}{ \sqrt{( { \sqrt{2} + \sqrt{6} })^{2} } } \\ = \frac{1}{ \sqrt{5} - \sqrt{6} } - \frac{1}{ \sqrt{5} + \sqrt{2} } - \frac{1}{ \sqrt{2} + \sqrt{6} } \\ = \frac{1( \sqrt{5} + \sqrt{6}) }{( \sqrt{5} - \sqrt{6} )( \sqrt{5} + \sqrt{6} ) } - \frac{1( \sqrt{5} - \sqrt{2}) }{( \sqrt{5} + \sqrt{2} )( \sqrt{5} - \sqrt{2} ) } - \frac{1( \sqrt{2} - \sqrt{6}) }{( \sqrt{2} + \sqrt{6} )( \sqrt{2} - \sqrt{6} ) } \\ = \frac{ \sqrt{5 } + \sqrt{6} }{ - 1} - \frac{ \sqrt{5} - \sqrt{2} }{3} - \frac{ \sqrt{2} + \sqrt{6} }{ - 4} \\ = \frac{ - 8 \sqrt{5} - 9 \sqrt{6} + or - 7 \sqrt{2} }{12} \\ or \\ = \frac{ - 8 \sqrt{5} - 9 \sqrt{6} - or + 7 \sqrt{2} }{12}$
$8. \\ \sqrt{7+4\sqrt{3}} + \sqrt{7-4\sqrt{3}} =4 \\ => \sqrt{ (\sqrt{3})^{2} + (\sqrt{4})^{2} + 2 \times 2 \times \sqrt{3}} + \sqrt{(\sqrt{3})^{2} + (\sqrt{4})^{2} - 2 \times 2 \times \sqrt{3}} = 4 \\ => \sqrt{ (\sqrt{3} + \sqrt{4})^{2}} + \sqrt{ ( -\sqrt{3} + \sqrt{4})^{2}} = 4 \\ => \sqrt{3} + \sqrt{4} -\sqrt{3} + \sqrt{4} = 4 \\ => \sqrt{4} + \sqrt{4} = 4 \\ => 2\sqrt{4} =4 \\ => \sqrt{4 \times 4}=4 \\ => \sqrt{16} = 4 \\ => 4=4$