Question

If the value of \(a - \dfrac{1}{{a - 5}} = 6\), then find the value of \(\left( {a - 5} \right)^3 - \dfrac{1}{{\left( {a - 5} \right)^3}}\)
1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 4 : 4

Given:

\(a - \dfrac{1}{{a - 5}} = 6\)

Formula used:

x - (1/x) = a

⇒ x³ - (1/x³) = a³ + 3a

Calculation:

\(a - \dfrac{1}{{a - 5}} = 6\)

On subtracting 5 both side, we get

\((a-5) - \dfrac{1}{{(a - 5)}} = 1\)

⇒ \((a-5)^3 - \dfrac{1}{{(a - 5)^3}} = 4\) 

∴ The value of \((a-5)^3 - \dfrac{1}{{(a - 5)^3}}\) is 4