# Try Newton sums, maybe!

Algebra Level 5

$\large{\begin{cases} x_1^2+x_2^2=5 \\ 3(x_1^5+x_2^5)=11(x_1^3+x_2^3) \end{cases}}$

Let $$F(x)$$ be a monic quadratic polynomial with real coefficients with real roots $$x_1$$ and $$x_2$$ that satisfy the system of equations above. If the product of all distinct value of $$F(3)$$ is $$\psi$$, find $$\sqrt{\psi - 4}$$.

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