Just 3 variables

Algebra Level 4

a,b,a,b, and xx are real numbers satisfying the following system of equations: a+b=3x2ab=4x23x4. \begin{aligned} a+b &=& 3x-2 \\ ab &=& 4x^2-3x-4. \end{aligned} What is the minimum value of a2+b2 a^2+b^2 (to three decimal places)?

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