Respostas

2013-10-20T23:21:03-02:00
x^2-2kx=1-3k\Longrightarrow x^2-2kx+3x-1=0

Para que a equação tenha raízes iguais, é necessário que \Delta=0. Então:

\Delta=0\Longrightarrow b^2-4\cdot a\cdot c=0\\\\
(-2k)^2-4\cdot1\cdot(3k-1)=0\Longrightarrow4k^2-12k+4=0\Longrightarrow k^2-3k+1=0\\\\
\Delta_2=b^2-4\cdot a\cdot c\\
\Delta_2=(-3)^2-4\cdot1\cdot1\\
\Delta_2=9-4\\
\Delta_2=5\\\\
k=\dfrac{-b\pm\sqrt{\Delta_2}}{2a}=\dfrac{3\pm\sqrt{5}}{2\cdot1}=\dfrac{3\pm\sqrt{5}}{2}\\\\\\
S=\{\dfrac{3-\sqrt{5}}{2},\dfrac{3+\sqrt{5}}{2}\}
3 3 3