Question

If 2x² + 4x - 2 = 0, then find x⁴ + 1/x⁴?
1. 38
2. 36
3. 34
4. 49

Answer 1

Correct Answer - Option 3 : 34

Given:

2x2 + 4x – 2 = 0

Formula used:

If x + 1/x = K

Then, x² + 1/x² = k² – 2

If x - 1/x = K

Then, x2 + 1/x2 = k2 + 2

Calculation:

Divide the given equation by x

⇒ 2x + 4 – 2/x = 0

⇒ 2x – 2/x = – 4

⇒ x – 1/x = – 2

Squar both side

⇒ x² + 1/x² = 4 + 2 = 6

Squar again

⇒ x⁴ + 1/x⁴ = 36 – 2

⇒ x4 + 1/x4 = 34

∴ The value of x⁴ + 1/x⁴ is 34.