[P+1]=[P]+1, Let [P]=n, then n is integer ∴([P+1,[P])=(n+1,n) lie inside the region of circles S1=x2+y2−2x−15=0,C1=(1,0),r1=4 and S2=x2+y2−2x−7=0,C2=(1,0),r2=2√2 Both circles are concentric. ∴(n+1)2+n2−2(n+1)−7>0 and (n+1)2+n2−2(n+1)−15<0⇒4<n2<8 Which is not possible for any integer.