Question
Question: If x2 + 6x – 27 \> 0, –x2 + 3x + 4 \> 0, then x lies in the interval...
If x2 + 6x – 27 > 0, –x2 + 3x + 4 > 0, then x lies in the interval
A
(3, 4)
B
[3, 4]
C
(–∞, 3] ∪ [4, ∞)
D
(−9, 4)
Answer
(3, 4)
Explanation
Solution
x2 + 6x – 27 > 0
⇒ x2 + 9x – 3x – 27 > 0
x(x + 9) –3(x + 9) > 0
⇒ (x – 3) (x + 9) > 0
x > 3 & x < – 9 ....(1)
–x2 + 3x + 4 > 0
⇒ x2 – 3x – 4 < 0
x2 – 4x + x – 4 < 0
⇒ x(x – 4) +1 (x – 4) < 0
(x – 4) (x + 1) < 0 ⇒ –1 < x < 4 ....(2)
from (1) and (2) (3, 4)