IIT JEE , AIEEE Forum - Mathematics , Algebra

gandhamkoushik

2x+2stepx=1 then x=

vinu

Hi gandhamkoushik,
u've x+?x=0.5 (where ? denotes step function)
we deduce from above eq that .....
x can't be =0 ,negative, greater than 0.5
& it is easy to check that it cannot be less than 0.5 too.......
So, the only solution to the eq is x=0.5 .

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

psr

u both r wrong

psr

u both r wrong
ans is k+0.5 where k is integer

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