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Solve 4{x} = x+ [x], x belongs to /R. The answer is x=0, 5/3. But I am getting xE [1,2). please explain with steps!

Solve 4{x} = x+ [x], x belongs to /R.
The answer is x=0, 5/3. But I am getting xE [1,2). 
please explain with steps!

Grade:12

2 Answers

pvn s
37 Points
8 years ago

x-{x}=[X]-----> something we know;

=>x-[x]={x}

That being said,

4{x}=x+[x]=>4(x-[x])=x+[x]

ie, 3x=5[x].---------(1)

Now, since RHS of (1) should be an integer(coz [x] is an integer),

 we can say x takes a fraction value as y/3 (so that 3x is integer),y is set of integers.

now substituting x as y/3 in (1) we get,the eqn

y=5[y/3]=>  y/5=[y/3]  =>RHS is integer,(same freaking logic) Therefore Y should be an multiple of 5

Thus we can narrow down as y being either 0 or 5 .

Now we can say that x as y/3 =>x=0,5/3.

Please upvote this if it helps, TC Smile

Sudharshan Jayakumar
39 Points
8 years ago

Perfect ! :)

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