Squared Inequality

Algebra Level 3

\(a,b,c\) are reals satisfying \(ab^2+bc^2+ca^2=3\). If the statement \[\dfrac{a^2+b^2}{c^2}+\dfrac{b^2+c^2}{a^2}+\dfrac{c^2+a^2}{b^2}\ge k\] is always true for some real number \(k\), then find the largest possible value of \(k\).

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