**If a + 1/a = p, prove that a**^{3} + 1/a^{3} = p (p^{2} – 3).

^{3}+ 1/a

^{3}= p (p

^{2}– 3).

**Answer :**

We know that

**a ^{3} + 1/a^{3} = (a + 1/a)^{3} – 3a (1/a) (a + 1/a)**

Substituting the values

a^{3} + 1/a^{3} = p^{3} – 3p

Taking p as common

a^{3} + 1/a^{3} = p (p^{2} – 3)

Therefore, it is proved.

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