Question

вычислить:
$sqrt{15+2 sqrt{26} } * sqrt{4+ sqrt{1+2 sqrt{26} } }*sqrt{4- sqrt{1+2 sqrt{26} } }$
$sqrt{ frac{11+ sqrt{21} }{11- sqrt{21} } } + sqrt{ frac{11- sqrt{21} }{11+ sqrt{21} } }$
разложить на множители
m+$sqrt{m}-6$
2y+$sqrt{y}-3$

Answer 1

$sqrt{(15+2sqrt{26}}cdot sqrt{4+sqrt{1+2sqrt{26}}}cdot sqrt{4-sqrt{1+2sqrt{26}}}} =\ sqrt{(15+2sqrt{26})(4-sqrt{1+2sqrt{26})}(4-sqrt{1+2sqrt{26})}} =\ sqrt{(15+2sqrt{26})( 16-( sqrt{1+2 sqrt{26} } )^2)}= sqrt{(15+2sqrt{26})(15-2 sqrt{26} )}} =\ sqrt{15^2-(2sqrt{26})^2}= sqrt{225-104}= sqrt{121}=11$


$sqrt{ frac{11+ sqrt{21} }{11- sqrt{21}} } + sqrt{ frac{11- sqrt{21} }{11+sqrt{21}}}= frac{ (sqrt{11+ sqrt{21}})^2+(sqrt{11- sqrt{21}})^2 }{ sqrt{(11- sqrt{21})(11+ sqrt{21})^ }}}=\\ frac{11+ sqrt{21}+11-sqrt{21} }{ sqrt{11^2-( sqrt{21} )^2} }= frac{22}{ sqrt{100}}= frac{22}{10}=2,2$


$m+ sqrt{m}-6= sqrt{m} sqrt{m} + sqrt{m}-2cdot3=( sqrt{m}+3)( sqrt{m}-2)$

$2y+ sqrt{y}-3=2 sqrt{y} sqrt{y}+ sqrt{y}-3cdot1= (2 sqrt{y}+3)( sqrt{y}-1)$

Answer 2

спасибо большое