X, Y and Z

Algebra Level 3

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

Given that \(x,y,z\) satisfy the equations above.

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

Details and Assumptions

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

\( \{ A \} \) deonte the fractional part of \(A\)

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