If x = 1/(4 – x), find the value of

If x = 1/(4 – x), find the value of

(i) x + 1/x

(ii) x³ + 1/x³

(iii) x⁶ + 1/x⁶

Answer 9

It is given that,

x = 1/(4 – x)

So,

(i) x(4 – x) = 1

4x – x² = 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) x³ + 1/x³ = (x + 1/x)² – 3(x + 1/x)

By substituting the values, we get

= (4)³ – 3(4)

= 64 – 12

= 52

(iii) x⁶ + 1/x⁶ = (x³ + 1/x³)² – 2

= (52)² – 2

= 2704 – 2

= 2702

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