Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Solution of inequatity
(x 2 – 10x + 22) > 0 is -
A
(– ∞ , 3)
B
(5 – 
, 3) ∪ (5 + 
, 7)
, 3) ∪ (5 + , 7)
C
(0, 5 – 
) ∪ (3, 4 )
) ∪ (3, 4 )
D
(7, ∞ )
Text Solution
Verified by ExpertsThe correct answer is:
D
Inequality 
(x 2 – 10x + 22) > 0 …(1)
L.H.S. is valid if :
x 2 – 10x + 22 > 0 
x < 5 – 
or x > 5 + 
x > 0
eq n (1) will be solved for two cases
(1) 0 < log 2 
< 1
⇒ 1 < 
< 2 = ⇒ 2 < x < 4
(x 2 – 10x + 22) > 0
x 2 – 10x + 22 < 1
x 2 – 10x + 21 < 0 ⇒ 3 < x < 7
The common solution 3 < x < 4
(2) log 2 
> 1 ⇒ 
> 2
x > 4
(x 2 – 10x + 22) > 0
x 2 – 10x + 22 > 1 ⇒ x 2 – 10x + 21 > 0
x < 3 or x > 7 common sol n x > 7
two cases x ∈ (3, 4) ∪ (7, ∞ )
Now common solution with initial values
x ∈ (7, ∞ )
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