**If x – 3 = 1/x, find the value of x**^{2} + 1/x^{2}.

^{2}+ 1/x

^{2}.

**Answer :**

It is given that

x – 3 = 1/x

We can write it as

x – 1/x = 3

Here

(x – 1/x)^{2} = x^{2} + 1/x^{2} – 2

So we get

x^{2} + 1/x^{2} = (x – 1/x)^{2} + 2

Substituting the values

x^{2} + 1/x^{2} = 3^{2} + 2

By further calculation

= 9 + 2

= 11

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