Question

Помогите решить!!!!!! ​

Answer 1

$1)\sqrt[3]{29\sqrt{2} -45}-\sqrt[3]{45+29\sqrt{2}}=\sqrt[3]{(\sqrt{2})^{3}-3*(\sqrt{2})^{2}*3+3*\sqrt{2}*3^{2}-3^{3}}-\sqrt[3]{3^{3}+3*3^{2}*\sqrt{2}+3*3*(\sqrt{2})^{2}+(\sqrt{2})^{3}}=\sqrt[3]{(\sqrt{2} -3)^{3}}-\sqrt[3]{(\sqrt{2}+3)^{3}}=\sqrt{2}-3-\sqrt{2}-3=-6$

$\sqrt[3]{38-17\sqrt{5}}+\sqrt[3]{17\sqrt{5} +38}=\sqrt[3]{2^{3}-3*2^{2}*\sqrt{5}+3*2*(\sqrt{5})^{2}-(\sqrt{5})^{3}}+$$\sqrt[3]{2^{3}+3*2^{2}*\sqrt{5}+3*2*(\sqrt{5})^{2}+(\sqrt{5})^{3}}=\sqrt[3]{(2-\sqrt{5})^{3}  }+\sqrt[3]{2+\sqrt{5})^{3}}=2-\sqrt{5}+2+\sqrt{5}=4$

$3)\sqrt[3]{170+78\sqrt{3}}-\sqrt[3]{78\sqrt{3}-170}=\sqrt[3]{(\sqrt{3})^{3}+3*(\sqrt{3})^{2}*5+3*\sqrt{3}*5^{2}+5^{3}}-\sqrt[3]{(\sqrt{3})^{3}-3*(\sqrt{3}){2}*5+3*\sqrt{3}*5^{2}-5^{3}}=\sqrt[3]{(\sqrt{3}+5)^{3}}-\sqrt[3]{(\sqrt{3}-5)^{3}} =\sqrt{3}+5-\sqrt{3}+5=10$