Quadratic Equation and Inequality

Algebra Level 4

Consider the equation \(x^2 + \lambda x + 1 = 0\) such that \(\lambda = (-\infty, -4]\bigcup[4, +\infty)\).

If \(\frac{4\lambda x}{x^2 + \lambda^2} \leq a\), find \(a\).

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