Question

The sum of 162^th power of the roots of the equation x³ – 2x² + 2x – 1 = 0 is ______.

Options

• 0

• 1

• 2

• 3

Answer 1

The sum of 162^th power of the roots of the equation x³ – 2x² + 2x – 1 = 0 is 3.

Explanation:

x³ – x² – x² + x + x – 1 = 0

⇒ x²(x – 1) – x(x – 1) + (x – 1) = 0

⇒ (x – 1) [x² – x + 1] = 0

⇒ x = 1, –ω, –ω²

So, sum = 1¹⁶² + (–ω)¹⁶² + (–ω²)¹⁶²

= 1 + 1 + 1  ...[∵ ω³ = 1]

= 3