Question

If x⁶ + x⁵ + x⁴ + x³ + x² + x + 1 = 0, then find the value of x⁵⁰⁵⁴ + x⁶⁰⁵⁵ - 7
1. 9
2. 5
3. -9
4. -5

Answer 1

Correct Answer - Option 4 : -5

Given:

x⁶ + x⁵ + x⁴ + x³ + x² + x + 1 = 0

Calculation:

Considering the given equation

x⁶ + x⁵ + x⁴ + x³ + x² + x + 1 = 0     -----(1)

In equation (1) multiplying by x

x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + x = 0     -----(2)

Equation (2) – (1)

⇒ x⁷ - 1 = 0

⇒ x⁷ = 1

x⁵⁰⁵⁴ + x⁶⁰⁵⁵ - 7

⇒ (x⁷)⁷²² + (x⁷)⁸⁶⁵ – 7

⇒ (1)⁷²² + (1)⁸⁶⁵ – 7

⇒ 1 + 1 – 7

⇒ - 5

∴ Required value is – 5