Giải phương trình: x^2-3x-1=0

`x^2-3x-1=0`

`<=>(x^2-3x+9/4)-13/4=0`

`<=>[x^2-2.x. 3/2+(3/2)^2]-(\sqrt{13}/2)^2=0`

`<=>(x-3/2)^2-(\sqrt{13}/2)^2=0`

`<=>(x-3/2-\sqrt{13}/2)(x-3/2+\sqrt{13}/2)=0`

`<=>(x-(3-\sqrt{13})/2)(x-(3+\sqrt{13})/2)=0`

`<=>`\(\left[ \begin{array}{l}x-\dfrac{3-\sqrt{13}}2=0\\x-\dfrac{3+\sqrt{13}}2=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=\dfrac{3-\sqrt{13}}2\\x=\dfrac{3+\sqrt{13}}2\end{array} \right.\)

`Vậy` `S={(3-\sqrt{13})/2;(3+\sqrt{13})/2}`