Let $\alpha, \beta$ be the roots of the equation $x^2+2 \sqrt{2} x-1=0$. The quadratic equation, whose roots are $\alpha^4+\beta^4$ and $\frac{1}{10}(\alpha^6+\beta^6)$, is:

<p>$$\begin{aligned} & x^2+2 \sqrt{2 x}-1=0 \\ & \alpha+\beta=-2 \sqrt{2} \text { and } \alpha \beta=-1 \\ & \alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \\ & =8+2=10 \\ & \alpha^4+\beta^4=\left(\alpha^2+\beta^2\right)^2-2(\alpha \beta)^2 \\ & =100-2=98 \\ & \alpha^6+\beta^6=\left(\alpha^2+\beta^2\right)^3-3 \alpha^2 \beta^2\left(\alpha^2+\beta^2\right) \\ & =1000-3(10) \\ & =970 \\ & \therefore \quad \frac{1}{10}\left(\alpha^6+\beta^6\right)=97 \end{aligned}$$</p> <p>Equation whose roots are $\alpha^4+\beta^4$ and $\frac{1}{10}\left(\alpha^6+\beta^6\right)$ is</p> <p>$$\begin{aligned} & x^2-(98+97) x+98 \times 97=0 \\ & x^2-195 x+9506=0 \end{aligned}$$</p>