Find the value of 2a3 + 2/a3

If (a² + 1)/a = 4, find the value of 2a³ + 2/a³

Answer :

It is given that,

(a² + 1)/a = 4

a²/a + 1/a = 4

a + 1/a = 4

So by multiplying the expression by 2a, we get

2a³ + 2/a³ = 2[a³ + 1/a³]

= 2 [(a + 1/a)³ – 3 (a) (1/a) (a + 1/a)]

= 2 [(4)³ – 3(4)]

= 2 [64 – 12]

= 2 (52)

= 104

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