Question

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Answer 1

Answer :-

Value of {x⁵ + (1/x⁵)} is 2525.

Explanation :-

x + (1/x) = 5

Finding x² + (1/x²)

We know that

{x + (1/x)}² = x² + (1/x²) + 2

⇒ (5)² = x² + (1/x²) + 2

⇒ 25 = x² + (1/x²) + 2

⇒ 25 - 2 = x² + (1/x²)

⇒ 23 = x² + (1/x²)

⇒ x² + (1/x²) = 23

Finding x³ + (1/x³)

We know that

{x + (1/x)}³ = x³ + (1/x³) + 3{x + (1/x)}

⇒ (5)³ = x³ + (1/x³) + 3(5)

⇒ 125 = x³ + (1/x³) + 15

⇒ 125 - 15 = x³ + (1/x³)

⇒ 110 = x³ + (1/x³)

⇒ x³ + (1/x³) = 110

Finding x⁵ + (1/x⁵)

We know that

{x⁵ + (1/x⁵)} = {x³ + (1/x³)}{x² + (1/x²)} - {x + (1/x)}

⇒ {x⁵ + (1/x⁵)} = (110)(23) - 5

⇒ {x⁵ + (1/x⁵)} = 2530 - 5

⇒ {x⁵ + (1/x⁵)} = 2525

∴ the value of {x⁵ + (1/x⁵)} is 2525.

Answer 2

Answer:

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