GS. 3 If the roots of $x^{2}-2 x-R=0$ differs by 12 , find the value of $R$.
$\begin{array}{l}\alpha+\beta=2, \alpha \beta=-R \\ \alpha-\beta=12 \\ \Rightarrow(\alpha-\beta)^{2}=144 \\ \Rightarrow(\alpha+\beta)^{2}-4 \alpha \beta=144 \\ \Rightarrow 4+4 R=144 \\ \Rightarrow R=35\end{array}$