Question

pls solve this que.
Thnks in advance.

Answer 1

You have an answer already. To add some detail to it, for x∈Z
x+2x2+1>13⟹x2−3x−5<0⟹(x−32)2<294⟹x⩽4
Similarly, 0<x−3x2−4<110⟹
Case x2>4: gives from 0<x−3x2−4⟹x>3

Case x2<4: gives from x−3x2−4<110⟹(x−5)2<−9(×)
So we are left with x=4 as the only possibility.