Logarithmic Inequality

Algebra Level 5

Find all values of the parameter aR a \in \mathbb{R} for which the following inequality is valid for all xR:x \in \mathbb{R}:

1+log5(x2+1)log5(ax2+4x+a).1+\log _{ 5 }{ { (x }^{ 2 }+1) } \ge \log _{ 5 }{ (a{ x }^{ 2 }+4x+a) }.

If the range of values of aa can be expressed in the form of (A,B], (A,B], then find the value of A+B. A + B.

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