MHB Calculating Real $(x,y,z)$ with System of Equations

[juantheron]

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,

please Help me

Thanks

 

[I like Serena]

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,

please 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...