Three distinct real numbers, a, b, c are in G.P. such that a + b+ c= x b, then
0 < x < 1
-1<x<3
x<-1 or x>3
-1<x<2
a + ar + ar2 = x. ar
or, r2 + r (1-x) + 1 = 0, r is real
Δ > 0 i.e.(1−x)2- 4 > 0
Or, x2-2x-3 > 0
Or, (x+1) (x-3) > 0
⇒ x < -1 or x > 3