Question

If x⁴ - 2x² - 3 = 0, find one of the values of x.
1. √3
2. 3
3. 5
4. √5

Answer 1

Correct Answer - Option 1 : √3

Calculation:

x4 - 2x2 - 3 = 0

Let, x² = t

⇒ t² - 2t - 3 = 0

⇒ t² - 3t + t - 3 = 0

⇒ t(t - 3) + 1(t - 3) = 0

⇒ (t - 3) (t + 1) = 0

⇒ t = 3, -1

Now t = x²

⇒ x² = 3

⇒ x = ± √3

x = √3      ----(1)

x² = -1

The above value is imaginary and there is no option given like that.

x = √3

∴ One of the values of x is √3.