# Just 3 variables

Algebra Level 4

$$a,b,$$ and $$x$$ are real numbers satisfying the following system of equations: $\begin{eqnarray} a+b &=& 3x-2 \\ ab &=& 4x^2-3x-4. \end{eqnarray}$ What is the minimum value of $$a^2+b^2$$ (to three decimal places)?

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