**If x = 1/(4 – x), find the value of**

(i) x + 1/x

(ii) x^{3} + 1/x^{3}

(iii) x^{6} + 1/x^{6}

**Answer 9**

It is given that,

x = 1/(4 – x)

So,

**(i)** x(4 – x) = 1

4x – x^{2} = 1

Now let us divide both sides by x, we get

4 – x = 1/x

4 = 1/x + x

1/x + x = 4

1/x + x = 4

**(ii)** x^{3} + 1/x^{3} = (x + 1/x)^{2} – 3(x + 1/x)

By substituting the values, we get

= (4)^{3} – 3(4)

= 64 – 12

= 52

**(iii)** x^{6} + 1/x^{6} = (x^{3} + 1/x^{3})^{2} – 2

= (52)^{2} – 2

= 2704 – 2

= 2702

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