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

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

Answer :

It is given that

x – 3 = 1/x

We can write it as

x – 1/x = 3

Here

(x – 1/x)² = x² + 1/x² – 2

So we get

x² + 1/x² = (x – 1/x)² + 2

Substituting the values

x² + 1/x² = 3² + 2

By further calculation

= 9 + 2

= 11

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