# Is the question right ?

Algebra Level 5

\large \begin{cases} \begin{align*} x+y+z&=4 \\ x^2+y^2+z^2&=6 \end{align*} \end{cases}

If $$x,y$$ and $$z$$ are real numbers that satisfy the equation above, and that they lie in the range of $$\left [ \frac ab, \frac cd \right]$$ for positive integers $$a,b,c$$ and $$d$$ such that $$\gcd(a,b) = \gcd(c,d) = 1$$, find the value of $$a+b+c+d$$.

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