Question

If x2 + x2 = 14, then find the value of x6-1/x6

Answer 1

$\huge\purple {\mathfrak{Bonjour Mate!}}$

GIVEN, x² + 1/x² = 14.

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We know, a²+b² = (a+b)² - 2 ab

So, (x+1/x) ² - 2 = 14

=> (x+1/x) = √16 = 4

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We also know, a²+b² = (a-b)² + 2 ab

So, (x-1/x)² + 2 = 14

=> (x - 1/x) = √12

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Ultimately, x² - 1/x²

= (x + 1/x) (x - 1/x)

= 4√12