Oblicz

[peresbmw]

Oblicz \(\sin \alpha + \cos \alpha\) jeśli \(\sin \alpha \cos \alpha = \frac{1}{4}\) , \(\alpha \in (180^ \circ, 270^ \circ) \)

[eresh]

Oblicz \(\sin \alpha + \cos \alpha\) jeśli \(\sin \alpha \cos \alpha = \frac{1}{4}\) , \(\alpha \in (180^ \circ, 270^ \circ) \)

\(\sin\alpha+\cos\alpha=x\\
(\sin\alpha+\cos\alpha)^2=x^2\\
\sin^2\alpha+2\sin\alpha\cos\alpha+\cos^2\alpha=x^2\\
1+2\cdot \frac{1}{4}=x^2\\
\frac{3}{2}=x^2\\
x=-\frac{\sqrt{3}}{\sqrt{2}}\)