Question

Найдите значения выражений.
Помагите даю 50 баллов

Answer 1

$(\frac{ \sqrt{5} }{ \sqrt{5}-2 }- \frac{5}{2+ \sqrt{5} } )*(5+ \sqrt{5} )= \frac{2 \sqrt{5}+5-5 \sqrt{5}+10}{5-4} * (5+ \sqrt{5}) =$$=(15-3 \sqrt{5} )(5+ \sqrt{5})=3(5- \sqrt{5})(5+ \sqrt{5})=3(25-5)=3*20=60$

$( \frac{ \sqrt{7} }{ \sqrt{7} + \sqrt{27} }- \frac{ \sqrt{3} }{ \sqrt{7}- \sqrt{27}})*(1-2 \sqrt{21} )=( \frac{ \sqrt{7} }{ \sqrt{7} +3 \sqrt{3} }- \frac{ \sqrt{3} }{ \sqrt{7}-3 \sqrt{3} } })*(1-2 \sqrt{21})=$$= \frac{7-3 \sqrt{21}- \sqrt{21} -9 }{7-27} *(1-2 \sqrt{21} )= \frac{(2+4 \sqrt{21})(1-2 \sqrt{21}) }{20}= \frac{2(1+2 \sqrt{21})(1-2 \sqrt{21}) }{20}$$= \frac{1-84}{10}=-8,3$

$(\frac{4}{3- \sqrt{11} }- \frac{ \sqrt{11} }{ \sqrt{11} +3} )* \frac{23- \sqrt{11} }{259} = \frac{4 \sqrt{11}+12-3 \sqrt{11}+11 }{9-11}* \frac{23- \sqrt{11} }{259}= \frac{ \sqrt{11}+23 }{-2}*$$* \frac{23- \sqrt{11} }{259}= \frac{529-11}{-2*259}=- \frac{518}{2*259}=-1$

$(\frac{ \sqrt{13} }{ \sqrt{13}- \sqrt{2} }+ \frac{ \sqrt{2} }{ \sqrt{13} + \sqrt{2} })* \frac{2 \sqrt{26} -11}{17} = \frac{13+ \sqrt{26} + \sqrt{26}-2 }{13-2}* \frac{2 \sqrt{26}-11 }{17}= \frac{2 \sqrt{26}+11 }{11}*$$* \frac{2 \sqrt{26}-11 }{17} = \frac{104-121}{11*17}=- \frac{17}{11*17}=- \frac{1}{11}$