P(a2,a+1) L1=3x−y+1=0 Origin and P lies same side w.r.t. L1 ⇒L1(0)⋅L1(P)>0 ∴3(a2)−(a+1)+1>0
2L1:3x−y+1=0 ⇒3a2−a>0 a∈(−∞,0)∪(
1
3
,∞)...........(1) Let L2:x+2y−5=0 Origin and P lies same side w.r.t. L2 ⇒L2(0)⋅L2(P)>0 ⇒a2+2(a+1)−5<0 ⇒a2+2a−3<0 ⇒(a+3)(a−1)<0 ∴a∈(−3,1)...........(2) Intersection of (1) and (2) a∈(−3,0)∪(