# System of equations in 3 variables

Algebra Level pending

Given that $$x,y,$$ and $$z$$ are real numbers that satisfy the following system of equations

$x+y+z=5$ $x^2+y^2+z^2=15$ $xy=z^2$

find the value of

$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$

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