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Q) Solve the equation x^3-[x]=3 ,where [x] denotes the integral part of the number x.
Asked by Anish | 27 Dec, 2018, 09:58: AM
answered-by-expert Expert Answer
Given equation :-  x3 - [x] = 3 .................(1)
 
Let x = [x]+f , where [x] is integer part and f is fraction. hence [x] = x - f ..............(2)
 
substituting for [x] using eqn.(2) in eqn.(1), we have,  x3 -x = 3-f .............(3)
 
from (3), we can write,   2< ( x3 - x ) < 3  .......................(4)
 
if x = -2, ( x3 - x ) = -6
if x = -1, ( x3 - x ) = 0
if x = 0, ( x3 - x ) = 0
if x = 1, ( x3 - x ) = 0
if x = 2, ( x3 - x ) = 6
 
hence the condition given in eqn.(4) is satisfied, if 1 < x < 2
 
hence [x] = 1   and given equation is x3 - 1 = 3   or   x3 = 4  or    begin mathsize 12px style x space equals space cube root of 4 end style
Answered by Thiyagarajan K | 29 Dec, 2018, 23:41: PM

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