If a2 – 3a + 1 = 0, find

If a² – 3a + 1 = 0, find

(i) a² + 1/a²

(ii) a³ + 1/a³.

Answer :

It is given that

a² – 3a + 1 = 0

By dividing each term by a

a + 1/a = 3

(i) We know that

(a + 1/a)² = a² + 1/a² + 2

It can be written as

a² + 1/a² = (a + 1/a)² – 2

Substituting the values

= 3² – 2

= 9 – 2

= 7

(ii) We know that

(a + 1/a)³ = a³ + 1/a³ + 3 (a + 1/a)

It can be written as

a³ + 1/a³ = (a + 1/a)³ – 3 (a + 1/a)

Substituting the values

= 3³ – 3 (3)

= 27 – 9

= 18

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