System of equations.

[jagdish]

solve all Real solution of System of equations

$x+y=\sqrt{4z-1}$

$y+z=\sqrt{4x-1}$

$z+x=\sqrt{4y-1}$

[Moon]

With some work you can prove that $x=y=z=1/2$ is the only solution.
Substitution like $x=a+\frac{1}{4}$ etc. might be useful!

[jagdish]

Thanks Admin Got it