Quadratic With Inequality Insane Level!

Algebra Level 5

The values of kk for which the inequality x2+k2k(x+6)1\dfrac{x^2+k^2}{k \cdot (x+6)} \geq 1 is satisfied by all x(1,1)x \in (-1,1) are [a,)[a, \infty).

Find the value of aa (round off up to 3 decimal places).

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