If a- \frac{1}{a-3}=5, then the value of (a-3)^{3}- {1}/{(a-3)^{3}}is

SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 53 of 100

Marks: +1, -0

a- {1}/{a-3}=5,

then the value of

(a-3)^{3}- {1}/{(a-3)^{3}}

Solution:

(4)

a- {1}/{(a-3)}=5

⇒(a-3)- {1}/{(a-3)}=2

On cubing both sides,

\{(a-3)- {1}/{(a-3)} \}^{3}=8

⇒(a-3)^{3}- ( {1}/{a-3} )^{3}-3 ×(a-3)

( {1}/{a-3} ) ((a-3)- {1}/{(a-3)}\ )=8

[∵(a-b)^{3}=a^{3}-b^{3}-3 a b(a- b ) ]

⇒(a-3)^{3}- ( {1}/{a-3} )^{3}-3 × 2=8

⇒(a-3)^{3}- ( {1}/{a-3} )^{3}=8+6=14

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