Question

The set of values of x for which the inequalities
${x}^{2} - 3x - 10$
,
$10x - {x}^{2} - 16 > 0$
hold simultaneously
A) (-2,5)
B) (2,8)
C) (-2,8)
D) (2,5)
​

Answer 1

Step-by-step explanation:

The set of values of x for which the inequalities

${x}^{2} - 3x - 10$

,

$10x - {x}^{2} - 16 > 0$

hold simultaneously

A) (-2,5)

B) (2,8)

C) (-2,8)

D) (2,5)

Answer 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