Question

determinati valorile reale ale lui x daca aria triunghiului ABO este 3 stiind ca A(x,1),B(2x,-1),O(0,0).

Answer 1

$A(x,1);\quad B(2x-1);\quad O(0,0); \\ \\ S = \dfrac{|\Delta|}{2} \\ \\ \Delta = \left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_O&y_O&1\end{array}\right| = \left|\begin{array}{ccc}x&1&1\\2x&-1&1\\0&0&1\end{array}\right|= -x+0+0-0-0-2x \Rightarrow \\ \\ \Rightarrow \Delta = -3x \\ \\ S = 3 \Rightarrow \dfrac{|-3x|}{2} = 3 \Rightarrow |-3x| = 6 \Rightarrow |3x| = 6 \Rightarrow \\ \Rightarrow 3x = \pm 6 \Rightarrow x = \pm 2 \Rightarrow \boxed{x\in\Big\{-2,2\Big\}}$