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System of equations

jacks

Well-known member
Apr 5, 2012
226
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
Mar 5, 2012
8,780
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...