TargetIIT

Find the number of solutions of the system of equations :
{x}+y+[z] = 2.3,
[y]+{z}+x = 4.5,
{y}+[x]+z=6.2
where {} and [] denote the fractional and greatest integer function respectively. Also find the solutions

some1 plz try dis

is it something like u add all the 3 eqns and u get

x+y+z = 6.5

wat is the answer ?

so is the answer infinte solutions..........[hide]m not sure at all ...by the way wats the answer/?[/hide]

Ans....only 1 solution (4.3, 0, 2.2)

no its nt frm YG file

I rmmbr this as a problem by Titu

Add up all three and get x+y+z=13.

Subtract the first eqn from the above to obtain

[x] +{z} = 10.7

From this can you argue that [x] = 10 and {z} = 0.7?

And also complete the problem?

Ans:- [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7Bx%20%5Cright%5C%7D+y%20+%5Cleft%5Bz%20%5Cright%5D%3D2.3[/im] .........(1) [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5By%20%5Cright%5D+%5Cleft%5C%7Bz%20%5Cright%5C%7D+x%3D4.5[/im] ..........(2) [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7By%20%5Cright%5C%7D+%5Cleft%5Bx%20%5Cright%5D+z%3D6.2[/im] ..........(3) add (1) and (2) and (3) we get [im]http://codecogs.izyba.com/gif.latex?x+y+z+%28%5Cleft%5Bx%20%5Cright%5D+%5Cleft%5C%7Bx%20%5Cright%5C%7D%29+%28%5Cleft%5By%20%5Cright%5D+%5Cleft%5C%7By%20%5Cright%5C%7D%29+%28%5Cleft%5Bz%20%5Cright%5D+%5Cleft%5C%7Bz%20%5Cright%5C%7D%29%3D%202.3+4.5+6.2[/im] and we now that [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5Bx%20%5Cright%5D+%5Cleft%5C%7Bx%20%5Cright%5C%7D%3Dx[/im] similarly for y and z we get [im]http://codecogs.izyba.com/gif.latex?2%28x+y+z%29%3D13[/im] [im]http://codecogs.izyba.com/gif.latex?%28x+y+z%29%3D6.5[/im] ........(4) subtract (1) from (4)
[im]http://codecogs.izyba.com/gif.latex?%28x-%5Cleft%5C%7Bx%20%5Cright%5C%7D%29+%28z-%5Cleft%5Bz%20%5Cright%5D%29%3D6.5-2.3[/im]
[im]http://codecogs.izyba.com/gif.latex?%5Cleft%5Bx%20%5Cright%5D+%5Cleft%5C%7Bz%20%5Cright%5C%7D%3D4.2[/im] or [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5Bx%20%5Cright%5D%3D4[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7Bz%20%5Cright%5C%7D%3D0.2[/im]

 means Integer part of x is equal to 4 and fractional part of z =0.2
similarly sub (2) from (4) we get
and [im]http://codecogs.izyba.com/gif.latex?%similarly sub (2) from (4) we get [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7Bx%20%5Cright%5C%7D+%5Cleft%5Bz%20%5Cright%5D%3D2.0[/im] [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5Bz%20%5Cright%5D%3D2[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7Bx%20%5Cright%5C%7D%3D0.0[/im] similarly sub (3) from (4) we get [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5By%20%5Cright%5D+%5Cleft%5C%7Bx%20%5Cright%5C%7D%3D0.3[/im] or [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5By%20%5Cright%5D%3D0[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7Bx%20%5Cright%5C%7D%3D0.3[/im] so final value of [im]http://codecogs.izyba.com/gif.latex?x%3D%5Cleft%5Bx%20%5Cright%5D+%5Cleft%5C%7Bx%20%5Cright%5C%7D%3D4+0.3%3D4.3[/im] [im]http://codecogs.izyba.com/gif.latex?y%3D%5Cleft%5By%5Cright%5D+%5Cleft%5C%7By%5Cright%5C%7D%3D0+0.2%3D0.2[/im]

sorry for my mistakes.........