Question

please answer the question​

Answer 1

hi mate

here is your answer

There are two inequalities and

both must hold simultaneously.

The first inequality gives

(x + 1)2 > 5x − 1

⇒ x2 + 2x + 1 > 5x − 1

⇒ x2 − 3x + 2 > 0

⇒ (x − 1) (x − 2) > 0

⇒ x ∈ (− ∞, 1) ∪(2, ∞) ... (1)

The second inequality gives

(x + 1)2 < 7x − 3

⇒ x2 − 5x + 4 < 0

⇒ (x − 1) (x − 4) < 0

⇒ x ∈ (1, 4)

Since both inequalities are to hold good, combining results of Eq. (1) and (2), we get

x ∈(2, 4) or 2 < x < 4

hope it helped ✌❤

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