If (x + 1/x)2 = 3, find x3 + 1/x3.

If (x + 1/x)² = 3, find x³ + 1/x³.

Answer :

It is given that

(x + 1/x)² = 3

(x + 1/x) = ± √3

We know that

x³ + 1/x³ = (x + 1/x)³ – 3 (x + 1/x)

Substituting the values

x³ + 1/x³ = (± √3)³ – 3 (± √3)

By further calculation

x³ + 1/x³ = (± 3√3) – (± 3√3) = 0

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