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MATHS CALCULUS
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Find the number of integral values of x satisfying √-x²+10x-16 < x-2
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A
3
💡 Explanation:
√−x² +10x−16
<x−2
∴−x
2
+10x−16≥0
x
2
−10x+16≤0
(x−2)(x−8)≤0
x∈[2,8]…(1)
−x
2
+10x−16
<x−2
squaringonbothsides
−x
2
+10x−16<x
2
−4x+4
2x
2
−14x+20>0
x
2
−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