Really Exponential

Algebra Level 2

Let α\alpha and β\beta be the two roots of the exponential equation 4×8x+1×0.251+5x21=0.4 \times 8^{x+1} \times 0.25^{1+5x^2}-1=0. What is the value of α2+β2?\alpha^2+\beta^2?

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