Nếu $\cos x + \sin x = \frac{1}{2}$ và \({0^0} &...

B

- Hướng dẫn giải

$\begin{array}{l} {\left( {\sin \alpha  + \cos \alpha } \right)^2} = {\sin ^2}\alpha  + 2\sin \alpha .\cos \alpha  + {\cos ^2}\alpha  = 1 + 2\sin \alpha .\cos \alpha \\  \Rightarrow \sin \alpha .\cos \alpha  = \frac{{{{\left( {\sin \alpha  + \cos \alpha } \right)}^2} - 1}}{2} =  - \frac{3}{8}\\  \Rightarrow \left\{ \begin{array}{l} \sin \alpha  = \frac{{1 + \sqrt 7 }}{4}\\ \cos \alpha  = \frac{{1 - \sqrt 7 }}{4} \end{array} \right. \Rightarrow \tan \alpha  =  - \frac{{4 + \sqrt 7 }}{3} \end{array}$

Suy ra (p;q)=(4;7)