# System of equations

#### jacks

##### Well-known member
Calculation of Real $(x,y,z)$ in

$x[x]+z\{z\}-y\{y\} = 0.16$

$y[y]+x\{x\}-z\{z\} = 0.25$

$z[z]+y\{y\}-x\{x\} = 0.49$

where $[x] =$ Greatest Integer of $x$ and $\{x\} =$ fractional part of x

My try:: Add $(i) + (ii)+(iii)$

$x[x]+y[y]+z[z] = 0.9$

Now I did not Understand How Can I proceed after that,

plz Help me

Thanks

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Calculation of Real $(x,y,z)$ in

$x[x]+z\{z\}-y\{y\} = 0.16$

$y[y]+x\{x\}-z\{z\} = 0.25$

$z[z]+y\{y\}-x\{x\} = 0.49$

where $[x] =$ Greatest Integer of $x$ and $\{x\} =$ fractional part of x

My try:: Add $(i) + (ii)+(iii)$

$x[x]+y[y]+z[z] = 0.9$

Now I did not Understand How Can I proceed after that,

plz Help me

Thanks
Hi jacks!

It seems to me that you need to get rid of all those "greatest integer" and "fractional part" thingies.
What draws my attention is that they only occur in conjunction with the same variable.
Perhaps it is useful to consider that $x^2=x([x]+\{x\})=x[x]+x\{x\}$?
You might for instance subtract (iii) from (i) and apply that...