If $\mathrm{\alpha },\mathrm{\beta }$ are the irrational roots of the equation ${\mathrm{x}}^5–5{\mathrm{x}}^4+9{\mathrm{x}}^3–9{\mathrm{x}}^2+5\mathrm{x}–1=0$, then the roots of the equation $\left(\mathrm{\alpha }+\mathrm{\beta }\right){\mathrm{x}}^2+2\mathrm{\alpha \beta x}-\mathrm{\alpha \beta }=0$ are

$\begin{array}{l}Let\alpha =\frac{3+\sqrt{5}}{2},\beta =\frac{3-\sqrt{5}}{2}\\ \therefore \alpha +\beta =3,\alpha \beta =\frac{9-5}{4}=1\\ \therefore (\alpha +\beta )x^2+2\alpha \beta x-\alpha \beta =0\\ \Rightarrow 3x^2+2x-1=0\\ \Rightarrow 3x^2+3x-x-1=0\\ \Rightarrow 3x(x+1)-1(x+1)=0\\ \Rightarrow (x+1)(3x-1)=0\\ \Rightarrow x=-1,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\end{array}$