If x + 1/x = 6, find

If x + 1/x = 6, find

(i) x – 1/x

(ii) x² – 1/x².

Answer :

(i) We know that

(x – 1/x)² = x² + 1/x² – 2

It can be written as

(x – 1/x)² = x² + 1/x² + 2 – 4

(x – 1/x)² = (x + 1/x)² – 4

Substituting the values

(x – 1/x)² = 6² – 4 = 32

So we get

x – 1/x = ± √32 = ± 4√2

(ii) We know that

x² – 1/x² = (x – 1/x) (x + 1/x)

Substituting the values

x² – 1/x² = (± 4√2) (6) = ± 24 √2

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