Вычислить [tex]12*( \sqrt[3]{3 \sqrt{3} } - \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3} + \sqrt{7}

Вычислить [tex]12*( \sqrt[3]{3 \sqrt{3} } - \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3} + \sqrt{7} )-6 \sqrt{21} [/tex]
- Предмет:
  Алгебра
- Автор:
  vargas99
- 6 лет назад

Ответы 1

$12*( \sqrt[3]{3 \sqrt{3} }- \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3}+ \sqrt{7} )-6 \sqrt{21} =$ $=12*\frac{\sqrt[3]{3^1*3^{\frac{1}{2} }}- \sqrt[5]{7^2*7^{\frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=12*\frac{\sqrt[3]{3^{1+ \frac{1}{2} }}- \sqrt[5]{7^{2+ \frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$ $=12*\frac{\sqrt[3]{3^{\frac{3}{2} }}- \sqrt[5]{7^{\frac{5}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21} =12*\frac{(3^{\frac{3}{2}})^ \frac{1}{3} - (7^{\frac{5}{2}})^ \frac{1}{5} }{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$ $=12*\frac{3^{\frac{3}{2}* \frac{1}{3}} - 7^{\frac{5}{2}*\frac{1}{5}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21} =12*\frac{3^{\frac{1}{2}} - 7^{\frac{1}{2}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$ $=6*2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-6* \sqrt{21} =6*(2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-\sqrt{21})=$ $=6*(2*\frac{ (\sqrt{3}- \sqrt{7})*(\sqrt{3}- \sqrt{7}) }{ (\sqrt{3}+ \sqrt{7})*(\sqrt{3}- \sqrt{7}) }-\sqrt{21})=$ $=6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{3^2-7^2}-\sqrt{21}) =6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{9-49}-\sqrt{21})=$ $=6*(2*\frac{ (\sqrt{3})^2-2* \sqrt{3}* \sqrt{7}+( \sqrt{7} )^2}{-40}-\sqrt{21})=$ $=6*(-\frac{2*(3-2* \sqrt{3*7}+7)}{2*20}-\sqrt{21}) =6*(-\frac{7+3-2* \sqrt{21}}{20}-\sqrt{21})=$ $=6*(-\frac{2*5-2* \sqrt{21}}{2*10}-\sqrt{21}) =6*(-\frac{2*(5-\sqrt{21})}{2*10}-\sqrt{21})=$ $=6*(-\frac{5-\sqrt{21}}{10}-\sqrt{21})=-6(\frac{5-\sqrt{21}}{10}+\frac{10*\sqrt{21}}{10})=$ $=-6*\frac{5-\sqrt{21}+10 \sqrt{21} }{10} =-6*\frac{5+9\sqrt{21}}{10} =-\frac{2*3*(5+9\sqrt{21})}{2*5}=$ $=-\frac{3*(5+9\sqrt{21})}{5} =-\frac{3*5+3*9\sqrt{21}}{5} =-\frac{15+27\sqrt{21}}{5}$
- Автор:
  isaiahvxfv
- 6 лет назад
- 0
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