Question

Иррациональные уравнения

Answer 1

1. 1) $frac{(sqrt{6}+sqrt{14})^{2}}{10+sqrt{84}}=frac{6+2sqrt{84}+14}{10+2sqrt{21}}=frac{6+2*2sqrt{21}+14}{10+2sqrt{21}}=frac{6+4sqrt{21}+14}{10+2sqrt{21}}=frac{20+4sqrt{21}}{10+2sqrt{21}}=frac{(20+4sqrt{21})(10-2sqrt{21})}{16}=frac{4(5+sqrt{21})*2(5-sqrt{21})}{16}=frac{(5+sqrt{21})*2(5-sqrt{21})}{4}=frac{(5+sqrt{21})(5-sqrt{21})}{2}=frac{25-21}{2}=frac{4}{2}=2$
 2) $frac{sqrt[3]{3}sqrt[3]{18}}{sqrt[3]{2}} = frac{sqrt[3]{54}}{sqrt[3]{2}}= frac{3sqrt[3]{2}}{sqrt[3]{2}}=3$
  3) $sqrt[4]{64}sqrt[12]{64}=sqrt[12]{64^{3}}sqrt[12]{64}=sqrt[12]{64^{3}*64}= sqrt[12]{64^{4}}=sqrt[3]{64}=4$