Question

решите пожалуйста с подробным описанием

Answer 1

$1) frac{ sqrt{2} }{2 sqrt{3}+4 sqrt{2} }= frac{ sqrt{2}(2 sqrt{3}-4 sqrt{2})}{(2 sqrt{3}+4 sqrt{2})( 2 sqrt{3}-4 sqrt{2})}=[(a-b)(a+b)=a ^{2}-b ^{2}]= \= frac{ sqrt{2}(2 sqrt{3}-4 sqrt{2})}{(2 sqrt{3}) ^{2} -(4 sqrt{2}) ^{2} } = frac{ 4 sqrt{6}-4}{12 -32 } = frac{1 - sqrt{6}}{5}$

$2) frac{3}{2- sqrt[3]{2} }= frac{3(2^{2}+2 sqrt[3]{2}+ sqrt[3]{2^{2}})}{(2- sqrt[3]{2})(2^{2}+2 sqrt[3]{2}+ sqrt[3]{2^{2}) }}=[(a-b)(a ^{2}+ab+b^{2})=a^{3}-b^{3}]= \ \ =frac{3(2^{2}+2 sqrt[3]{2}+ sqrt[3]{2^{2}})}{(2) ^{3} - (sqrt[3]{2})^{3} }}=frac{3(4+2 sqrt[3]{2}+ sqrt[3]{4)}}{8-2}=frac{4+2 sqrt[3]{2}+ sqrt[3]{4}}{2}=2+ sqrt[3]{2}+ frac{ sqrt[3]{4} }{2}$