**If a**^{2} – 3a + 1 = 0, find

^{2}– 3a + 1 = 0, find

(i) a^{2} + 1/a^{2}

(ii) a^{3} + 1/a^{3}.

**Answer :**

It is given that

a^{2} – 3a + 1 = 0

By dividing each term by a

a + 1/a = 3

##### (i) We know that

**(a + 1/a) ^{2} = a^{2} + 1/a^{2} + 2**

It can be written as

a^{2} + 1/a^{2} = (a + 1/a)^{2} – 2

Substituting the values

= 3^{2} – 2

= 9 – 2

= 7

##### (ii) We know that

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

It can be written as

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

Substituting the values

= 3^{3} – 3 (3)

= 27 – 9

= 18

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