\[\boxed{\text{362\ (362).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ x^{4} - 6x^{2} + 3 = 0\]
\[x = \sqrt{3 + \sqrt{5}}:\]
\[\left( \sqrt{3 + \sqrt{5}} \right)^{4} - 6 \cdot\]
\[\cdot \left( \sqrt{3 + \sqrt{5}} \right)^{2} + 3 = 0\]
\[\left( 3 + \sqrt{5} \right)^{2} - 6 \cdot \left( 3 + \sqrt{5} \right) + 3 = 0\]
\[9 + 6\sqrt{5} + 5 - 18 - 6\sqrt{5} + 3 = 0\]
\[- 1 \neq 0 \Longrightarrow \sqrt{3 + \sqrt{5}} - не\ \]
\[является\ корнем.\]
\[\textbf{б)}\ x^{4} - 10x^{2} + 23 = 0\]
\[x = \sqrt{5 - \sqrt{2}}:\]
\[\left( \sqrt{5 - \sqrt{2}} \right)^{4} - 10 \cdot\]
\[\cdot \left( \sqrt{5 - \sqrt{2}} \right)^{2} + 23 = 0\]
\[\left( 5 - \sqrt{2} \right)^{2} - 10 \cdot \left( 5 - \sqrt{2} \right) +\]
\[+ 23 = 0\]
\[25 - 10\sqrt{2} + 2 - 50 + 10\sqrt{2} +\]
\[+ 23 = 0\]
\[0 = 0 \Longrightarrow \sqrt{5 - \sqrt{2}} - является\ \]
\[корнем.\]