The roots of the equation (x²-2 2 x+1=0) are

The discriminant of the equation ((-2 \sqrt{2})^2-4(1)(1)=8-4=4 \gt 0) and $a$ perfect square, so roots are real and different but we can't say that roots are rational because coefficients are not rational therefore. ($\frac{\sqrt{2 \sqrt{2} \pm \sqrt{(2 \sqrt{2})^2-4}}}{2}=\frac{2 \sqrt{2} \pm 2}{2}=\sqrt{2} \pm$1) this is irrational (\therefore) the roots are real and different.