iran-konkur 2014 Q107

iran-konkur · Other · konkur-riazi_1393 Curve Sketching Number of Solutions / Roots via Curve Analysis
107- For which values of $x$ in the domain of $y=\sqrt{5+4x-x^2}$, does the graph of $y=\sqrt{5+4x-x^2}$ lie above the graph of $y=|x-3|+2$?
(1) $\left(\dfrac{3-\sqrt{17}}{2},\ 5\right)$ (2) $\left(2,\ \dfrac{3+\sqrt{17}}{2}\right)$
(3) $\left(2,\ \dfrac{4+\sqrt{15}}{2}\right)$ (4) $\left(2,\ 2+\sqrt{15}\right)$
\textbf{107-} For which values of $x$ in the domain of $y=\sqrt{5+4x-x^2}$, does the graph of $y=\sqrt{5+4x-x^2}$ lie above the graph of $y=|x-3|+2$?

\medskip
(1) $\left(\dfrac{3-\sqrt{17}}{2},\ 5\right)$ \hfill (2) $\left(2,\ \dfrac{3+\sqrt{17}}{2}\right)$

(3) $\left(2,\ \dfrac{4+\sqrt{15}}{2}\right)$ \hfill (4) $\left(2,\ 2+\sqrt{15}\right)$

\medskip