Question

question in the photo​

Answer 1

Answer:

Option (a) is correct

Step-by-step explanation:

We are given inequality,

⇒ x²( x + 2 ) ( x - 1 )³ ( x² + 1 ) > 0

Here the critical points are x = 0, x = -2 and x = 1.

We get 4 intervals ( - ∞, -2 ) , ( -2, 0 ) , ( 0, 1 ), ( 1, ∞ ).

By substituting values from each intervals in the given inequality, we found that only intervals ( - ∞, -2 ) and ( 1, ∞ ) satisfies the given inequality.

1 and -2 are not included in the solution set.

So the required answer is,

⇒ x ∈ ( -∞, -2) U ( 1 , ∞ )