$\sin x+\cos x=\dfrac{5}{4}$
$\Leftrightarrow \sin^2x+2\sin x\cos x+\cos^2x=\Big(\dfrac{5}{4}\Big)^2$
$\Leftrightarrow 1+2\sin x\cos x=\dfrac{25}{16}$
$\Leftrightarrow \sin x\cos x=\dfrac{9}{32}$
Mà $\sin x+\cos x=\dfrac{5}{4}$
$\Leftrightarrow (\sin x;\cos x)=\Big(\dfrac{5+\sqrt7}{8};\dfrac{5-\sqrt7}{8}\Big); \Big(\dfrac{5-\sqrt7}{8};\dfrac{5+\sqrt7}{8}\Big)$
