Answer:
x = 5 and -6
Step-by-step explanation:
Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.
Hence:
let
a = 6, b = 5, c = x+1 and d = x
Therefore, ab = cd
6*5 = x(x+1)
30 = x²+x
x²+x - 30 = 0
x²+ 6x - 5x - 30 = 0
x(x+6) - 5(x+6) =0
(x-5)(x+6) = 0
x-5 =0 and x+6 = 0
x = 5 and -6
