Find the value of 3×3 + 5x – 3/x3 – 5/x.

If x² + 1/x² = 27, find the value of 3x³ + 5x – 3/x³ – 5/x.

Answer :

We know that

(x – 1/x)² = x² + 1/x² – 2

Substituting the values

(x – 1/x)² = 27 – 2 = 25

So we get

x – 1/x = ± √25 = ± 5

Here

3x³ + 5x – 3/x³ – 5/x = 3 (x³ – 1/x³) + 5 (x – 1/x)

It can be written as

= 3 [(x – 1/x)³ + 3 (x – 1/x)] + 5 (x – 1/x)

Substituting the values

= 3 [(± 5)³ + 3 (± 5)] + 5 (± 5)

By further calculation

= 3 [(± 125) + (± 15)] + (± 25)

So we get

= (± 375) + (± 45) + (± 25)

= ± 445

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