If x-3+[1 /(x-3)]=4, then what is the value of (x-3)^{3}+ [1 /(x-3)^{3 ] ?

SSC CGL 12 Aug 2017 Shift 1 Paper

Question : 63 of 100

Marks: +1, -0

x-3+[1 /(x-3)]=4,

then what is the value of

(x-3)^{3}+ [1 /(x-3)^{3 ] ?

Solution:

(x-3)+ {1}/{(x-3)}=4

On cubing both sides,

⇒(x-3)^{3}+ {1}/{(x-3)^{3}}

+3 [(x-3)+ {1}/{(x-3)} ]=64

∴ (x-3)^{3}+ {1}/{(x-3)^{3}}

=64-3 ×4=52

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