**If x – 1/x = 3 + 2√2, find the value of ¼ (x**^{3} – 1/x^{3})

^{3}– 1/x

^{3})

**Answer :**

It is given that,

x – 1/x = 3 + 2√2

So,

x^{3} – 1/x^{3} = (x – 1/x)^{3} + 3(x – 1/x)

= (3 + 2√2)^{3} + 3(3 + 2√2)

By using the formula, (a+b)^{3} = a^{3} + b^{3} + 3ab (a + b)

= (3)^{3} + (2√2)^{3} + 3 (3) (2√2) (3 + 2√2) + 3(3 + 2√2)

= 27 + 16√2 + 54√2 + 72 + 9 + 6√2

= 108 + 76√2

Hence,

¼ (x^{3} – 1/x^{3}) = ¼ (108 + 76√2)

= 27 + 19√2

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