Question

if x-1/X=5 find the value of x²+1/x² and x⁴ +1/x⁴​

Answer 1

Answer:

Given x + 1/x = 5

Squaring, (x + 1/x)² = 5² = 25

Or, expanding x² + 2.x.1/x + 1/x² = 25

Or, x² + 2 + 1/x² = 25

Transposing 2 to right and simplifying

x² + 1/x² = 23……………………………………………………………….(1)

Now

x⁴ + 1/x⁴ = [(x²)² + 2.x². 1/x² + (1/x²)²] - 2.x². 1/x² = (x² + 1/x²)² - 2

= 23² - 2 [Substituting for x² + 1/x² from (1)]

= 529 - 2 = 527 (Proved)

Answer 2

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