The set of values of x for which the inequalities
,
hold simultaneously
A) (-2,5)
B) (2,8)
C) (-2,8)
D) (2,5)
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Step-by-step explanation:
The set of values of x for which the inequalities
,
hold simultaneously
A) (-2,5)
B) (2,8)
C) (-2,8)
D) (2,5)
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Answered by
2
Step-by-step explanation:
x2 – 3x – 10 < 0 ⇒ (x + 2) (x – 5) < 0 ⇒ (x – (–2)) (x – 5) < 0 ⇒ x∈ (–2, 5) (If a < b, then (x – a) (x – b) < 0 ⇒ a < x < b) 10x – x2 – 16 > 0 ⇒ x2 – 10x + 16 < 0 ⇒ (x – 2) (x – 8) < 0 ⇒ x∈ (2, 8) (If a < 0, then (x – a) (x – b) < 0 ⇒ a < x < b) ∴ x∈ (–2, 5) ∩ (2, 8) ⇒ x∈ (2, 5).Read more on Sarthaks.com - https://www.sarthaks.com/995052/the-set-of-values-of-x-for-which-the-inequalities-x-2-3x-10-0-10x-x-2-16-0-hold-simultaneously-is?show=995057#a995057
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