Let α and β are roots of the equation x2+ax+1=0 So, α+β=−a and αβ=1 given |α−β|<√5 ‌⇒√(α−β)2−4αβ<√5 ‌(‌ as ‌(α−β)2=(α+β)2−4αβ) ‌⇒√a2−4<√5 ‌⇒a2−4<5 ‌⇒a2−9<0⇒a2<9 ‌⇒−3<a<3 ‌⇒a∈(−3,3)
