IIT JEE , AIEEE Forum - Mathematics , Algebra

puneet

hiiiiii

Is ur question .. to solve the equation 2.x + 2.[x] = 1

well if yes . thn ...

let us try ...

we take few cases

case 1: x > 1/2

so 2[x] >= 0

also 2x > 1

and thus 2.x + 2.[x] = 1 is not possible ..

case 2: 0<=x<1/2

[x] = 0 in this case

and 2x<1

thus 2.x + 2.[x] = 1 is again not possible ..

case 3: x < 0

[x] <= -1

and 2x < 0

so, again 2.x + 2.[x] = 1 is not possible ..

case 4: x = 1/2

Now [x] = 0

and 2x = 1

thus, 2x + 2[x] = 2.(1/2) + 0 =1

and thus the only solution is x = 1/2 ..

I hope this helps u ..

cheers