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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