Chapter: Similarity· Mathematics Part 2 (Geometry)
Answer: x = 4
By the basic proportionality theorem, \(\dfrac{AD}{DB} = \dfrac{AE}{EC}\).
\(\dfrac{x}{x - 2} = \dfrac{x + 2}{x - 1}\) \(\therefore x(x - 1) = (x + 2)(x - 2)\)
\(\therefore x^2 - x = x^2 - 4\) \(\therefore x = 4\).
Check: AD = 4, DB = 2, AE = 6, EC = 3; \(\dfrac{4}{2} = \dfrac{6}{3} = 2\). All lengths are positive, so x = 4 is valid.