If x lies between -1 and 1, then which of the following is true?

x^{2} - 1 > 0

x^{2} + 1 > 0

x^{2} + x > 0

- x2 - 1 > 0 and x2 + 1 > 0
- x2 + 1 > 0 and x2 + x > 0
- Only x2 + 1 > 0
- All three are correct

Option 3 : Only x2 + 1 > 0

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**Calculations:**

x lies between -1 and 1,

Let x = 0

⇒ x2 - 1 = (0)^{2} - 1 = -1

-1 < 0

⇒ x2 - 1 > 0 is not true

Similarly, x2 + 1 > 0

⇒ x2 + 1 = (0)2 + 1 = 1

1 > 0

⇒ x2 + 1 > 0 is true

Similarly, x2 + x = (0)^{2} + 0 = 0

⇒ x2 + x > 0 is not true

**∴ The correct relation is x2 + 1 > 0.**

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