**If x + 1/x = 3 1/3, find the value of x**^{3} – 1/x^{3}

^{3}– 1/x

^{3}

**Answer :**

It is given that,

x + 1/x = 3 1/3

we know that,

(x – 1/x)^{2} = x^{2} + 1/x^{2} – 2

= x^{2} + 1/x^{2} + 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,

x^{3} – 1/x^{3} = (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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