If x – 1/x = 5, find the value of x4 + 1/x4.

If x – 1/x = 5, find the value of x⁴ + 1/x⁴.

Answer :

We know that

(x – 1/x)² = x² + 1/x² – 2

It can be written as

x² + 1/x² = (x – 1/x)² + 2

Substituting the values

x² + 1/x² = 5² + 2 = 27

Here

x⁴ + 1/x⁴ = (x² + 1/x²)² – 2

Substituting the values

x⁴ + 1/x⁴ = 27² – 2

So we get

= 729 – 2

= 727

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