X, Y and Z

Algebra Level 4

x+[y]+{z}=4.3y+[z]+{x}=5.5z+[x]+{y}=6.4 \begin{aligned} x+\left[ y \right] +\left\{ z \right\} &=& 4.3\\ y+\left[ z \right] +\left\{ x \right\} &=& 5.5\\ z+\left[ x \right] +\left\{ y \right\} &=& 6.4\\ \end{aligned}

Given that x,y,zx,y,z satisfy the equations above.

What is the value of (20xyz)2{ \left( \frac { 20xy }{ z } \right) }^{ 2 }?

Details and Assumptions

[A] \left [ A \right ] denote the greatest integer function of AA

{A} \{ A \} deonte the fractional part of AA

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