Find the value of x3 – 1/x3

If x + 1/x = 3 1/3, find the value of x³ – 1/x³

Answer :

It is given that,

x + 1/x = 3 1/3

we know that,

(x – 1/x)² = x² + 1/x² – 2

= x² + 1/x² + 2 – 4

= (x + 1/x)² – 4

But x + 1/x = 3 1/3 = 10/3

So,

(x – 1/x)² = (10/3)² – 4

= 100/9 – 4

= (100 – 36)/9

= 64/9

x – 1/x = √(64/9)

= 8/3

Now,

x³ – 1/x³ = (x – 1/x)³ + 3 (x) (1/x) (x – 1/x)

= (8/3)³ + 3 (8/3)

= ((512/27) + 8)

= 728/27

= 26 26/27

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