# If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a) ? Given a³

| If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a) ?

A. 31

B. 26

C. 28

D. 24

### Right Answer is: C

#### SOLUTION

Given a³ + 3a² + 9a = 1 ………..(i)

Multiply the equation by a:

a^{4} + 3a^{3} + 9a^{2} = a …………(ii)

Multiply the eqn(i) by 3:

3a^{3} + 9a^{2} + 27a = 3 …………(iii)

⇒ a^{4} + 3a^{3} + 90a = a ………..(iv)

Eqn (iv) – (iii):

a^{4} – 27a = a – 3

⇒ a^{4} = 28a – 3

Dividing the whole equation by a:

a^{3} + 3/a = (a^{4} +3)/a

Put the value of a^{4}:

(28a – 3 + 3)/a = 28

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