Exponential inequality

Algebra Level 2

Suppose that α<x<β\alpha < x< \beta is the solution to the following inequality: (13)x2+1>(19)x+2.\left(\frac{1}{3}\right)^{x^2+1} > \left(\frac{1}{9}\right)^{x+2}. Then what is the value of βα? \beta - \alpha ?

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