The sum of all integral values of k (k=0) for which the equation x−12−x−21=k2 in x has no real roots, is
Answer: 66
Solutions · 1
Official solution
Clearing denominators: 2x2−(6+k)x+3k+4=0 (for x=1,2). No real roots requires (k+6)2−8(3k+4)<0⟹k2−12k−4<0⟹(k−6)2<32⟹6−42<k<6+42.
Integral k∈{1,2,…,11}, sum =66.