\frac{(\frac{1+\sqrt{51}} {\sqrt{7}} )^4+(\frac{1-\sqrt{51}}{\sqrt{7}})^4 }{\frac{1+\sqrt{51}}{\sqrt{7}}*\frac{1-\sqrt{51}}{\sqrt{7}}} = \\=\frac{\frac{1+4\sqrt{51}+306+204\sqrt{51}+51^2}{49}+\frac{1-4\sqrt{51}+306-204\sqrt{51}+51^2}{49}} {\frac{(1+\sqrt{51})(1-\sqrt{51})}{7}} =\frac{\frac{307+2*51^2+307}{49}} { \frac{-50}{7} }=\frac{307+51^2}{7(-35)} =\\=-\frac{2908}{175}" alt="\frac{a^3}{b} +\frac{b^3}{a}= \frac{a^4+b^4}{ab} =>\frac{(\frac{1+\sqrt{51}} {\sqrt{7}} )^4+(\frac{1-\sqrt{51}}{\sqrt{7}})^4 }{\frac{1+\sqrt{51}}{\sqrt{7}}*\frac{1-\sqrt{51}}{\sqrt{7}}} = \\=\frac{\frac{1+4\sqrt{51}+306+204\sqrt{51}+51^2}{49}+\frac{1-4\sqrt{51}+306-204\sqrt{51}+51^2}{49}} {\frac{(1+\sqrt{51})(1-\sqrt{51})}{7}} =\frac{\frac{307+2*51^2+307}{49}} { \frac{-50}{7} }=\frac{307+51^2}{7(-35)} =\\=-\frac{2908}{175}" align="absmiddle" class="latex-formula">