Question

If x + x^-1 = 4, then the value of \(\dfrac{\left(x^3+x^{-1}\right)}{\left(x^2-3x+1\right)}\) is:
1. 14
2. 12
3. 13
4. 11

Answer 1

Correct Answer - Option 1 : 14

Given:

x + x-1 = 4 or x² + 1 = 4x

Calculation:

⇒ \(\dfrac{\left(x^3+x^{-1}\right)}{\left(x^2-3x+1\right)}\)= (x⁴ + 1)/x(4x - 3x) = (x⁴ + 1)/x² = x² + 1/x² ..... (1)

⇒ x + 1/x = 4 ..... (2)

⇒ By squaring both side of equation (2)

⇒ x² + 1/x² + 2 = 16

⇒ x2 + 1/x² = 14 ..... (3)

∴ The result will be 14.