**If x – 1/x = 5, find the value of x**^{4} + 1/x^{4}.

^{4}+ 1/x

^{4}.

**Answer :**

We know that

**(x – 1/x) ^{2} = x^{2} + 1/x^{2} – 2**

It can be written as

x^{2} + 1/x^{2} = (x – 1/x)^{2} + 2

Substituting the values

x^{2} + 1/x^{2} = 5^{2} + 2 = 27

Here

x^{4} + 1/x^{4} = (x^{2} + 1/x^{2})^{2} – 2

Substituting the values

x^{4} + 1/x^{4} = 27^{2} – 2

So we get

= 729 – 2

= 727

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