JEE Class main Answered
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
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 
Answered by Thiyagarajan K | 29 Dec, 2018, 11:41: PM
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