Question

If x + 1/x = 1, then find the value of x⁶ + 3x¹² + 5x¹⁸ + 7x²⁴.
1. 16
2. 10
3. 8
4. 6

Answer 1

Correct Answer - Option 1 : 16

Given: 

We have the equation x + (1/x) = 1

Formula used:

If x + 1/x = 1 then x3 = -1

Calculation:

x6 + 3x12 + 5x18 + 7x24

⇒ (x3)2 + 3(x³)⁴ + 5(x3)⁶ + 7(x³)⁸

⇒ (-1)2 + 3(-1)4 + 5(-1)6 + 7(-1)⁸

⇒  1 + 3 + 5 + 7

⇒ 16

∴ The value of x6 + 3x12 + 5x18 + 7x24 is 16.