The biquadratic equation two of whose roots are $1 + \mathrm{i}, 1 – \sqrt{2}$ is

$\begin{array}{l}If1+i,1-\sqrt{2}arerootsthen\\ 1-i,1+\sqrt{2}arealsoroots\\ \therefore TheEquationis(x-(1+i))(x-(1-i))(x-(1+\sqrt{2}))(x-(1-\sqrt{2}))=0\\ \Rightarrow (x^2-2x+2)(x^2-2x-1)=0\\ \Rightarrow x^4-2x^3-x^2-2x^3+4x^2+2x+2x^2-4x-2=0\\ \Rightarrow x^4-4x^3+5x^2-2x-2=0\end{array}$