IIT JEE , AIEEE Forum - Mathematics , Algebra

mudita

the no of sol 4 the equation...

|[x]-2x|=3

is ....

catch_arnnie

i think there are 2 solutions..

this is how i've done --->

|[x]-2x|=3

=> [x] - 2x = 3 or [x] - 2x = -3

=> [x] = 2x + 3 or [x] = 2x - 3

since. LHS is an interger in the above equations, therefore RHS has to be an integer, & for that, x has to be an integer or x should be 1/2

but x = 1/2 does not give the solution

=> x has to be an interger

so, [x] = x

=> x = -3 or x = 3

therefore, there are 2 solutions

plz correct me if i'm wrong anywhere ....

waterdemon

I do not agree with Catch_arnie
There will be two solutions but not that are given above

there will be two cases
1)[x]=2x+3
2)[x]=2x-3

We know that [x] can be written as (-1-x) so putting the value of [x] in both the above cases we get two solutions
x=-4/3 or x=2/3.
please correct me if I am wrong

catch_arnnie

Mr. waterdemon, tell me how can you write [x] as (-1-x) ??

[x] means greatest interger function of x, so, you cannot write [x] = (-1-x)

waterdemon

No offenses dude
just got off the track
my mistake

waterdemon

I agree with ur answer

mudita

THE ANSWER IS 4..THR ARE 4 SOL.

mudita

HEY CATCH_ARNIE MY ANS WAS ALSO COMIN 2 BT THE ANS . IS 4 SO I AM NT GETTIN THT HOW IT CAME?

catch_arnnie

the ans. can be wrong...
from which book hav u taken the question??

waterdemon

See udita I have tried the Question even by the graph mathod I think the answer is definitely 2 solutions in either case

mudita

it is a ques. 4m sample paper of resonsnce

waterdemon

hey mudita Now I am dam sur ethat the number of solutions is "2"

If u draw the graph of [x]=2x+3
then u will get one solution at x=-3

and if u draw [x]=2x-3
then u will get only one solution at x=3

Thus there are to solution taking both the cases.

plZ Rate me if I could solve ur problem.

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