Question

Please solve this problem​

Answer 1

The value in the square root will always be greater than or equal to 0. i.e x will be positive.

So, $\mathsf{{x^2 - 1 } {\geq{ 0 }}}$

$\implies{\mathsf{ x^2 {\geq{ 1}}}}$

• x ∈ ( - ∞ , - 1] ∪ [ 1, ∞ )

Now, $\mathsf{x^2 - 4 < 0}$

$\mathsf{ (x - 2) ( x + 2) < 0}$

$\implies{\mathsf{ x < - 2, 2}}$

• x ∈ (- 2, 2)

Answer will be x ∈ (-2, - 1) ∪ ( 1, 2).

Answer 2

kindly check the attachment for the stepwise solution and answer.

Do thank my answer if it is helpful.