If $$a - \frac{1}{{a - 5}} = 10$$ , then the value of $${\left( {a - 5} \right)^3} - \frac{1}{{{{\left( {a - 5} \right)}^3}}}$$ is:
A. 140
B. 70
C. 100
D. 120
Answer: Option A
Solution(By Examveda Team)
$$a - \frac{1}{{a - 5}} = 10$$We can write it is as (subtracting 5 from both sides)
$$\eqalign{ & a - 5 - \frac{1}{{a - 5}} = 10 - 5 \cr & {\text{Now, }}\left( {a - 5} \right) - \frac{1}{{\left( {a - 5} \right)}} = 5 \cr} $$
So, take the cube of this equation,
$$\eqalign{ & \left[ {{{\left( {a - 5} \right)}^3} - \frac{1}{{{{\left( {a - 5} \right)}^3}}}} \right] = 125 + 3 \times 5 \cr & \left[ {{{\left( {a - 5} \right)}^3} - \frac{1}{{{{\left( {a - 5} \right)}^3}}}} \right] = 140 \cr} $$
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