You will get the important questions
Find the number of integral values of x satisfying √-x²+10x-16 < x-2
√−x² +10x−16 <x−2
∴−x2 +10x−16≥0
x2 −10x+16≤0(x−2)(x−8)≤0
x∈[2,8]…(1)
−x2 +10x−16 <x−2
squaringonbothsides
−x2 +10x−16<x2 −4x+4
2x2 −14x+20>0
x2 −7x+10>0
(x−5)(x−2)>0
x∈(−∞,2)U(5,∞)…(2)
Points which lie in both the interval (1) and (2) are 6,7 and 8
∴x=6,7,8