If x – 2/x = 3, find the value of x3 – 8/x3.

If x – 2/x = 3, find the value of x³ – 8/x³.

Answer:

We know that

(x – 2/x)³ = x³ – 8/x³ – 3 (x) (2/x) (x – 2/x)

By further simplification

(x – 2/x)³ = x³ – 8/x³ – 6 (x – 2/x)

It can be written as

x³ – 8/x³ = (x – 2/x)³ + 6 (x – 2/x)

Substituting the values

x³ – 8/x³ = 3³ + 6 × 3

By further calculation

x³ – 8/x³ = 27 + 18 = 45

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