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}$