# Problem Of the Day-2

Here is Yesterday Problem

Yesterday Winner was Akash Agarwal

You must be knowing that If you win the Problem of the day for 4 times in a week – then I will send you a Really interesting book on any topic you want 🙂

Today’s Problem :

Find all possible values of x satisfying :

[x]/[x-2] – [x-2]/[x] = (8{x} + 12)/([x-2][x])

(.) = Normal bracket

{.} = Fractional part function

[.] = GIF/Floor function

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Posted on Wednesday,May 30, 2012, in Problems and tagged algebra, Problem, problem of the day, winner. Bookmark the permalink. 6 Comments.

-4

4 is the answer….

Solution:-

after seeing equation [x]/[x-2] – [x-2]/[x] = (8{x} + 12)/([x-2][x])

we got that x is an integer as

so {x}=0

so…

Now equation comes

[x]/[x-2] – [x-2]/[x] = (12)/([x-2][x])

now on solving it we get

x=4

The equation can be modified as

[x]^2-[x-2]^2 = 8{x}+12;

Now as LHS is an integer, RHS need to be an integer as well.

Thus, 8{x}=integer.

Now;

Let [x]=y;

Then,

4y-4 = 8{x}+16;

y = 2{x}+4;

As y is an integer the possible values of {x} can be 0 or 0.5;

For {x} = 0; y = [x] = 4; Thus x = 4; and

For {x} = 0.5; y = [x] = 5; Thus x = 5+0.5 = 5.5

Thus there are two possible values of x as 4 and 5.5 .

Is absolutely correct 🙂

Congratulations

You have answered 2 times correct 🙂

Hmmm sir… Akash.. U r from IIT Roorkee

Yes, I am from IIT Roorkee… 🙂