Вычислить [tex]12*( \sqrt[3]{3 \sqrt{3} } - \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3} + \sqrt{7} )-6 \sqrt{21} [/tex]. Created by asimx. algebra-ru

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Вычислить [tex]12*( \sqrt[3]{3 \sqrt{3} } - \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3} + \sqrt{7} )-6 \sqrt{21} [/tex]

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90misha90

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$12*( \sqrt[3]{3 \sqrt{3} }- \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3}+ \sqrt{7} )-6 \sqrt{21} =$

$=12*\frac{\sqrt[3]{3^1*3^{\frac{1}{2} }}- \sqrt[5]{7^2*7^{\frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=12*\frac{\sqrt[3]{3^{1+ \frac{1}{2} }}- \sqrt[5]{7^{2+ \frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$

$=12*\frac{\sqrt[3]{3^{\frac{3}{2} }}- \sqrt[5]{7^{\frac{5}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}
=12*\frac{(3^{\frac{3}{2}})^ \frac{1}{3} - (7^{\frac{5}{2}})^ \frac{1}{5} }{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$

$=12*\frac{3^{\frac{3}{2}* \frac{1}{3}} - 7^{\frac{5}{2}*\frac{1}{5}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}
=12*\frac{3^{\frac{1}{2}} - 7^{\frac{1}{2}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=$

$=6*2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-6* \sqrt{21}
=6*(2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-\sqrt{21})=$

$=6*(2*\frac{ (\sqrt{3}- \sqrt{7})*(\sqrt{3}- \sqrt{7}) }{ (\sqrt{3}+ \sqrt{7})*(\sqrt{3}- \sqrt{7}) }-\sqrt{21})=$

$=6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{3^2-7^2}-\sqrt{21})
=6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{9-49}-\sqrt{21})=$

$=6*(2*\frac{ (\sqrt{3})^2-2* \sqrt{3}* \sqrt{7}+( \sqrt{7} )^2}{-40}-\sqrt{21})=$

$=6*(-\frac{2*(3-2* \sqrt{3*7}+7)}{2*20}-\sqrt{21})
=6*(-\frac{7+3-2* \sqrt{21}}{20}-\sqrt{21})=$

$=6*(-\frac{2*5-2* \sqrt{21}}{2*10}-\sqrt{21})
=6*(-\frac{2*(5-\sqrt{21})}{2*10}-\sqrt{21})=$

$=6*(-\frac{5-\sqrt{21}}{10}-\sqrt{21})=-6(\frac{5-\sqrt{21}}{10}+\frac{10*\sqrt{21}}{10})=$

$=-6*\frac{5-\sqrt{21}+10 \sqrt{21} }{10}
=-6*\frac{5+9\sqrt{21}}{10}
=-\frac{2*3*(5+9\sqrt{21})}{2*5}=$

$=-\frac{3*(5+9\sqrt{21})}{5}
=-\frac{3*5+3*9\sqrt{21}}{5}
=-\frac{15+27\sqrt{21}}{5}$

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