Question 63

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

Solution

Given : $$x-3+[\frac{1}{(x-3)}]=4$$ ------------(i)

Cubing both sides, we get :

=> $$(x-3+[\frac{1}{(x-3)}])^3=(4)^3$$

=> $$(x-3)^3+(\frac{1}{x-3})^3+3(x-3)(\frac{1}{x-3})[(x-3)+(\frac{1}{x-3})]=64$$

=> $$(x-3)^3+(\frac{1}{x-3})^3+3(4)=64$$ [Using equation (i)]

=> $$(x-3)^3+[\frac{1}{(x-3)^3}]=64-12=52$$

=> Ans - (C)

Create a FREE account and get:

Free SSC Study Material - 18000 Questions
230+ SSC previous papers with solutions PDF
100+ SSC Online Tests for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Time Speed Distance Questions CAT Averages Questions CAT Time, Distance and Work Questions CAT Data Sufficiency Questions CAT Linear Equations Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Puzzles Questions CAT Miscellaneous LR Questions CAT DI with connected data sets Questions CAT DI Miscellaneous Questions CAT Data change over a period Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Jumbles Questions CAT Para Summary Questions CAT Grammar and Sentence Correction Questions CAT Miscellaneous Questions CAT Critical Reasoning Questions

Follow us on

Boost your Prep!

Download App