Find the range of values of x for which 8 + 2x - {x}^(2) \geqslant 0 \\ 5 {x }^(2) - x - 4 > 0 ​

Question

Find the range of values of x for which


`8 + 2x - {x}^(2) \geqslant 0 \\ 5 {x }^(2) - x - 4 > 0`
​

Answer 1

Explanation:

8 + 2x - x^2 >= 0

x^2 - 2x - 8 <= 0

(x - 1)^2 - 9 <= 0
(x - 1)^2 <= 9
x - 1 <= +- 3
-3 <= x - 1 <= 3
-2 <= x <= 4